Can a scriptwriter continue a Tv series that he didn't create?

(Homework question, can't seem to find it online)

Let's say, Fred is a scriptwriter.
When he was younger, he used to love the tv show 'Knight Rider'.

Now, many years later, he wants to make a continuation of that show,
that can be watched without having to watch the original Knight Rider.

Different characters, different car, but still kind of like the same
show, just a different version of it.

Is Fred allowed to do this?
Can he just continue a show (or kind of make a new version of it) that
he hasn't created himself, years after it aired?