You have two options here. One option is to convert the date value to a string and do a string comparison as follows:

IF (TO_CHAR(date_val,'YYYY') > '2000') THEN
   
END IF;

Another option is to use the TO_DATE function to convert the comparison string to a date value.

IF (date_val > TO_DATE('12/31/2000','MM/DD/YYYY')) THEN 
   
END IF;