There are a few hints in here which might help you on your way:

ALTER PROCEDURE [dbo].[TR_SearchTests_Counter_v2]

@REGISTER_IDint= null,

@PART_NUMBERnvarchar(50)= null,

@PHASE_NUMBERnvarchar(10)= null,

@TEST_NUMBERnvarchar(20) = null,

@PROCESS_ORDERnvarchar(50) = null,

@IS_VOIDbit= null,

@REGISTERED_FROMsmalldatetime= null,

@REGISTERED_TOsmalldatetime= null,

@TEST_STATUS_IDint= null,

@DEFECT_TYPE_IDint= null,

@DEFECT_POSITION_IDint= null,

@FILM_SIZE_IDint= null,

@OUT_RESULTintOUTPUT

AS

BEGIN

SET NOCOUNT ON;

-- >>> Reset empty values to null (fix for entity framework sending empty strings instead of nulls)

if @PART_NUMBER = ''

SET @PART_NUMBER = null

if @PHASE_NUMBER = ''

SET @PHASE_NUMBER = null

if @TEST_NUMBER = ''

SET @TEST_NUMBER = null

if @PROCESS_ORDER = ''

SET @PROCESS_ORDER = null

-- Returns distinct(/grouped by) TestId's matching search Criteria

SELECT @OUT_RESULT = COUNT(a.TestId)

--count(a.TestId) as ResultCount

FROM ( -- a

SELECT top 5000

t.TestId

FROM TR_Tests t

INNER JOIN TR_TestConfiguration tc

ON tc.TestConfigurationId = t.TestConfigurationId

INNER JOIN TR_Registers r

ON tc.RegisterId = r.RegisterId

INNER JOIN TR_PartPhases pp

ON tc.PartPhaseId = pp.PartPhaseId

INNER JOIN TR_Parts p

ON pp.PartId = p.PartId

INNER JOIN TR_YearPrefixes yp

ON DATEPART(year, tc.DateRegistered) = yp.Year -- non-SARGable predicate

CROSS APPLY ( -- x

SELECT TestNumberOut =

TestNumberPrefix +

yp.Prefix + -- can this be calculated? Then you could remove TR_YearPrefixes from the query

CONVERT(varchar(10), TestNumber) +

'/' +

RIGHT('000' + CONVERT(varchar(10), BatchReference),3)

) x

WHERE EXISTS ( -- d

SELECT 1

FROM TR_TestResults tr

INNER JOIN TR_FilmSizes_InTestResults fstr

ON tr.TestResultId = fstr.TestResultId

WHERE tr.TestId = t.TestId

AND (

(fstr.FilmSizeId = @FILM_SIZE_ID OR @FILM_SIZE_ID IS NULL)

OR (dtr.DefectTypeId = @DEFECT_TYPE_ID OR @DEFECT_TYPE_ID IS NULL)

OR (dtr.DefectPositionId = @DEFECT_POSITION_ID OR @DEFECT_POSITION_ID IS NULL)

)

) -- d

AND

(tc.RegisterId= @REGISTER_IDOR @REGISTER_IDIS NULL) AND

(p.PartNumber= @PART_NUMBEROR @PART_NUMBERIS NULL) AND

(pp.PhaseNumber= @PHASE_NUMBEROR @PHASE_NUMBERIS NULL) AND

(tc.ProcessOrder= @PROCESS_ORDEROR @PROCESS_ORDERIS NULL) AND

(tc.IsVoided= @IS_VOIDOR @IS_VOIDIS NULL) AND

(tc.DateRegistered>= @REGISTERED_FROMOR @REGISTERED_FROMIS NULL) AND

(tc.DateRegistered<= @REGISTERED_TOOR @REGISTERED_TOIS NULL) AND

(TR_Tests.TestStatusId = @TEST_STATUS_ID OR @TEST_STATUS_IDIS NULL) AND

(x.TestNumberOut LIKE '%' + @TEST_NUMBER + '%' OR @TEST_NUMBER IS NULL)

) a

OPTION (RECOMPILE) -- a new plan is generated each time the query is run

END

RETURN 0