If a person is registered under earlier law, whether he needs to be registered under GST law compulsorily

Yes. As per section 22 (2) of the CGST Act, every person who, on the day immediately preceding the appointed day, is registered or holds a license under an earlier law, shall be liable to be registered under this Act with effect from the appointed day.

(ICAI FAQ PUBLICATIONS 06-09-2017 REGISTRATION : FAQ NO. 2)