Not necessarily. If you choose to roll over/renew the CD for another term, the bank will pay interest according to the roll over or renewal terms of your account agreement.
Let's say you haven't decided in advance. Once the CD matures, you may have a grace period, established by the bank, to decide whether to renew the CD or withdraw the funds. The bank will pay interest, if any, once the CD matures in accordance with your account agreement and bank policy during the grace period.
You should review your account agreement, which explains if interest is paid after maturity. You should have received this agreement when you opened the account.