Tucker Carlson, private citizen, having a forum on Twitter that reaches 20 million people does not need to criticize Fox News or even mention their name.
If he wants his payout (and I imagine he does), it’s perfectly fair to have him sign a non-disparagement agreement.
It’s probably illegal to say he can’t speak in public about politics.
“It’s probably illegal to say he can’t speak in public about politics.”
A broad, potentially unconscionable contract term like that in a proposed settlement agreement would probably not survive attorney edits.