Are there any TLS Extensions that a server can *require* the client send?

This question is a bit of a follow on to this Q&A:

TLS 1.2 Handshake: Does the server have to take all extensions sent by the Client?

If the client sends an Extension that the server does not recognize, the server can simply ignore it and continue with a Server Hello — the client is then free to terminate the session if that particular extension was required by the client, or continue the handshake without that extension.

My question: Are there any TLS Extensions which some servers might choose to require, thereby responding to a Client Hello which doesn’t include those extensions by terminating the session?

Granted, this could be different on a deployment by deployment basis, but if there are some extensions that might be lend themselves to being required by the server, they would suffice as the answer to this question.