How to avoid spill data to tempdb

SELECT DISTINCT
        ( Column1 ) AS Column2 ,
        Function1(Column3) AS Column4
FROM    Object1 Object2
        INNER JOIN Object3 Object4 ON Object2.Column5 = Column6
WHERE   Column7 = ?
        AND LEFT(Column8, ?) = ? 
       GROUP BY Column1

…it's tricky to work out which column belongs to which table, but assuming the tables in question look something like this:

CREATE TABLE #Object1
(
    Column1 integer NULL,
    Column5 integer NULL,
    Column7 integer NULL,
    Column8 varchar(100) NULL,
);
 
CREATE TABLE #Object3
(
    Column3 integer NULL,
    Column6 integer NULL
);

…you can avoid the Sort completely by creating this index:

CREATE INDEX i
ON #Object1 (Column7, Column1)
INCLUDE (Column5, Column8);

This index allows a seek on the equality predicate on Column7, producing rows in Column1 order as required by the Stream Aggregate for the grouping operation. This is the main optimization. It seems like a suitable index for seeking already exists on the second table, something like:

CREATE INDEX i
ON #Object3 (Column6)
INCLUDE (Column3);

Given these indexes, the plan changes to:

From a style point of view:

1. The DISTINCT is redundant here, given the GROUP BY clause
2. You should use aliases on all column references in the query
3. The predicate using LEFT should be rewritten as a LIKE