This article explains the steps to get FaceTime working again.

The problem may be that the FaceTime icon isn't lighting up so you can use it, that it isn't appearing as an option at all when you make a call, or that you can't receive calls. The following issues could be the cause:

Make sure FaceTime is turned on. To check this, open the Settings app, scroll down to FaceTime, and toggle the FaceTime slider to on/green.

Make sure the person you’re calling has FaceTime. The person you’re calling will need to have FaceTime available and set up on their device in order to video chat with you. They’ll need an iPhone 4 or later, an iPod touch 4th generation or later, an iPad 2 or later, a modern Mac, or an Android/Windows device with a web browser. All of these devices must have a user-facing camera, which is required so the person you’re calling can see you.