Hey Bosko,
no, you do not. You're ssn does not ever expire unless it is revoked for some reason. Your new Ead will suffice for a new licence though.

TimeLine:
Expiration April 28, 2015
Renewal sent:Feb 10 (very late)
Renewal Rejected : Missed a question
RENEWAL Resent: Feb 25
Biometrics: March 27, Did a walk-in on March 23
Approved: April 3 ; New ead April 15