Why is the index not seeking?

Stored procedures that just select from a view always make me nervous. Best thing to fix this would be to remove the view from the equation and rewrite your stored procedure to select from base tables and having the proper filter on corresponding tables. If I was to rewrite it, it would look something like the code below. Additionally, if you don't need some columns in return set, you should consider removing them and tables that they come from completely from the code. Try to run the following code and compare output to original output of SP.

One last thing to consider. Parameter sniffing could be killing your performances especially since you are selecting from a view and a plan was created based on "bad" parameter, try RECOMPILE option to check if it gives you better plan that runs much faster.

 SELECT  UserId
       , ApplicationId
       , fullname
       , userstate
       , interviewDateTime
       , interviewerSelectedDate
       , lastlogin
       , ISNULL(firstPayment, 0) AS 'firstpaymentstatus'
       , transactionDate
       , ISNULL(applicationComplete, 0) AS 'applicationcomplete'
       , ISNULL(No_of_references, 0) AS 'no_of_references'
       , ISNULL(No_Of_UnreviewedNotes, 0) AS 'no_of_unreviewednotes'
       , ISNULL(int_report_complete, 0) AS 'int_report_complete'
       , Comment
       , CommentBy
       , ISNULL(interviewerViewed, 0) AS 'interviewerviewed'
       , IsInDemand
       , URI
       , DateOfBirth
       , earliestAvailabilityDate
       , Programme
       , fullTimeStudent
       , OrgType
       , [Status]
       , DBSstatusDescription
 FROM    (
           SELECT    ul.UserID
                   , app.ApplicationID
                   , ul.FirstName
                   , ul.LastName
                   , ul.Email
                   , ul.FirstName + ' ' + ul.LastName AS 'fullname'
                   , a.LastContact AS 'lastlogin'
                   , usm.StateName AS 'userstate'
                   , app.Programme
                   , app.InterviewerID
                   , app.Season
                   , ac.interviewerSelectedDate
                   , tpi.interviewDateTime
                   , tpi.interviewstatus
                   , ac.firstPayment
                   , ac.applicationComplete
                   , ref.No_of_references
                   , notes.No_Of_UnreviewedNotes
                   , ISNULL(ac.interviewReportComplete, 0) AS 'int_report_complete'
                   , at.transactionDate
                   , com.CommentBy
                   , com.Comment
                   , ac.interviewerViewed
                   , app.Returner
                   , app.rejected
                   , ul.createdOn
                   , app.requiresInterview
                   , CASE ISNULL(afm.applicationID, 0)
                       WHEN 0 THEN 0
                       ELSE 1
                     END AS 'IsInDemand'
                   , ul.CountryCode
                   , ul.RegionId
                   , upload.URI
                   , app.applicationRating
                   , ul.DateOfBirth
                   , app.earliestAvailabilityDate
                   , app.fullTimeStudent
                   , id.first_name + ' ' + id.last_name AS 'interviewerName'
                   , orgType.OrgType
                   , orgType.Status
                   , orgType.DBSstatusDescription
           FROM      tbl_UserLogin ul
           INNER JOIN tbl_applicant a
                     ON ul.ApplicantID = a.ApplicantID
           INNER JOIN tbl_application app
                     ON a.ApplicantID = app.ApplicantID
           INNER JOIN tbl_season s
                     ON s.Season = app.Season
                        AND s.Is_Current = 1
           INNER JOIN tbl_user_state_message usm
                     ON app.UserState = usm.UserState
           LEFT JOIN tbl_interviewer_details id --Consider INNER JOIN  if possible
                     ON id.interviewer_id = app.InterviewerID
           LEFT JOIN (
                       SELECT    appi.applicationID
                               , appiu.URI
                       FROM      tbl_application_images appi
                       INNER JOIN tbl_application_image_uploads appiu
                                 ON appi.imageID = appiu.imageID
                                    AND ( appi.[Type] = 1
                                          OR ( appi.[Type] IS NULL )
                                        )
                     ) upload
                     ON app.ApplicationID = upload.applicationID
           LEFT JOIN tbl_applicant_checklist ac
                     ON app.ApplicantID = ac.applicantID
           LEFT JOIN tbl_pending_interviews tpi
                     ON app.ApplicationID = tpi.applicationid
           LEFT JOIN (
                       SELECT    COUNT() AS 'No_of_references'
                               , applicationID
                       FROM      tbl_application_images tai
                       WHERE     tai.[Type] = 3
                                 AND tai.[Status] <> 0
                       GROUP BY  tai.applicationID
                     ) ref
                     ON ref.applicationID = app.ApplicationID
           LEFT JOIN (
                       SELECT    COUNT() AS 'No_Of_UnreviewedNotes'
                               , applicationID
                       FROM      tbl_application_document_notes adn
                       WHERE     adn.reviewed = 0
                       GROUP BY  adn.applicationID
                     ) notes
                     ON notes.applicationID = app.ApplicationID
           LEFT JOIN (
                       SELECT    cat.transactionDate
                               , cat.applicationID
                               , ROW_NUMBER() OVER ( PARTITION BY cat.applicationID ORDER BY cat.transactionDate DESC ) AS GroupRowNumber
                       FROM      COLAFinance.dbo.accountTransaction cat
                       WHERE     cat.feeTypeID = 1 -- AND cat.transactionDate >= DATEADD(YEAR,-1,GETDATE())
                       
                     ) at
                     ON at.applicationID = app.ApplicationID
                        AND at.GroupRowNumber = 1
           LEFT JOIN (
                       SELECT    sub.Comment
                               , sub.CommentBy
                               , sub.ApplicationID
                       FROM      (
                                   SELECT    ac.Comment
                                           , ac.CommentBy
                                           , ac.ApplicationID
                                           , ROW_NUMBER() OVER ( PARTITION BY ac.ApplicationID ORDER BY ac.CommentDateTime DESC ) AS GroupRowNumber
                                   FROM      tbl_application_comments ac
                                   WHERE     ac.CommentByType = 'INT'
                                             AND ac.CommentDateTime >= DATEADD(YEAR, -1, GETDATE())
                                 ) AS sub
                       WHERE     GroupRowNumber = 1
                     ) com
                     ON com.applicationID = app.ApplicationID
           LEFT JOIN (
                       SELECT DISTINCT
                                 ( applicationID )
                       FROM      tbl_application_filter_match
                     ) afm
                     ON afm.applicationID = app.ApplicationID
           LEFT JOIN (
                       SELECT TOP 1
                                 so.OrgType
                               , ch.Status
                               , rcs.DBSstatusDescription
                               , cid.ApplicationId
                       FROM      tbl_application_crb_initialData cid
                       INNER JOIN tbl_season_organisationId so
                                 ON cid.OrganisationId = so.OrgId
                       LEFT JOIN tbl_crbHistory ch
                                 ON cid.ClientReference = ch.ClientReference
                       LEFT JOIN ref_crbStatus rcs
                                 ON ch.Status = rcs.statusId
                       ORDER BY  cid.DateAdded DESC
                               , ch.DateAdded DESC
                     ) orgType
                     ON app.ApplicationID = orgType.ApplicationId
           WHERE     app.InterviewerID = @interviewerId
                     AND ( ( interviewDateTime IS NULL )
                           OR ( interviewstatus = 'REJD' )
                         )
         ) AS vw

There's no fundamental reason, it's just an optimizer limitation. It can do all the things you want: matching the filtered index, pushing predicates past window functions and so on, but asking it to also transform the outer join to an outer apply is a step too far.

Not all possible transformations have been coded into the optimizer for good reason. The most commonly needed and beneficial ones are mostly there, but when you come across a missing one like this, you need to perform the transformation yourself. Simply write the OUTER JOIN as an OUTER APPLY, for example:

 CREATE TABLE dbo.App
 (
     ApplicationID integer NOT NULL
 );
 
 CREATE TABLE dbo.accountTransaction
 (
     applicationID integer NOT NULL,
     transactionDate date NOT NULL,
     feetypeID integer NOT NULL
 );
 
 CREATE INDEX fi 
 ON dbo.accountTransaction (applicationID, transactionDate, feetypeID)
 WHERE feetypeID = 1;
     
 SELECT *
 FROM dbo.App AS A
 OUTER APPLY
 (
     SELECT 
         AT.transactionDate,
         AT.applicationID,
         GroupRowNumber =
             ROW_NUMBER() OVER (
             PARTITION BY AT.applicationID
             ORDER BY AT.transactionDate DESC)
     FROM dbo.accountTransaction AS AT
     WHERE
         AT.feetypeID = 1
         AND AT.applicationID = A.ApplicationID
 ) AS OA;

Execution plan: