Hi mahesh213,
In the ExpiryPeriod column save the period in Days (INT) form insterd of week or month. If you save week or month form then you need to check each possible value to convert it to days.
Refer below test Query and implement as per your table structure.
SQL
DECLARE @Id INT
IF EXISTS(SELECT Id FROM Expiry WHERE Id = @Id)
BEGIN
DECLARE @Date DATE, @Days INT
SET @Date = (SELECT [Date] FROM Expiry WHERE Id = @Id)
SET @Days = (SELECT ExpiryPeriod FROM Expiry WHERE Id = @Id)
SET @Date = DATEADD(DAY,@Days,@Date)
IF(@Date >= CONVERT(DATE,GETDATE()))
BEGIN
DELETE FROM Expiry WHERE Id = @Id
END
END