I’m sure the “legal” answer is, without permission, non of us can really use any clips from anything we’ve worked on, unless you own the production. If you had stipulated in a contract that you would be able to, obviously that is different. But just because we worked on a show, that doesn’t give us any special rights. (not that I’m aware of)
Typically a note to the producer who hired you, asking for permission, would be the best course of action.
A lot of us have good enough relationships with our clients that it isn’t that big of a deal, as long as the program/movie has been released or aired. But it never hurts to ask first.
As I read your post again, i’m wondering if you are actually asking about using footage from a show you didn’t work on, and doing your own composition for it, for demo purposes.
If so, that might be a bit misleading, and perhaps a bit sketchy. You would certainly have zero authority to rip and use the footage.