Blocking a chimney / fireplace

Name changed as this is outing to anyone that knows me IRL. Whilst I don’t care about this post I do about others
In the last year I took on 5 special needs cats via my work that otherwise wouldn’t be able to be rehomed. They get on swimmingly, everything is great.
However, we recently moved house and one of the cats has discovered the fireplace/chimney and I’m terrified of them climbing in and getting stuck. The old owners put an electric fire in the fireplace but left the original behind. The surveyor wasn’t concerned and said it was safe but now I have the issue of the cats.

Can I just block it with a piece of board or a grate? It’s hard to get access as obviously the electric fire is in front of it. But there’s a big enough gap for the cat.

My friend has two cats who are indoor cats and she has blocked hers off because one of them went up there and it took a while to coax it back out!

I had my chimney sorted out by https://emersonproservices.com/new-jersey/chimney-fireplace/ last fall after I kept getting smoke backing into the living room, and they handled the inspection and cleanup way quicker than I expected
Their tech walked me through what needed fixing without pushing extras, which I appreciated
If you’re trying to pin down what’s causing your issue, they’re pretty easy to reach and won’t blindside you on price