No. Your permanent resident card is proof enough of your eligibility to work in the U.S.
Andre Olivie, Esq.
Legal disclaimer: This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice. Do not rely on this advice without speaking to an immigration attorney in detail about your case. This message does not create an attorney-client relationship.
If you already have the permanent residence card, you no longer need, and cannot renew the EAD. if you have not yet received permanent residence, then you will need a valid EAD in order to work.
The statement above is general in nature, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship.