What would be the standard figured bass notation for a dominant 7th chord on A with a key signature of g minor (ie the 3rd needs to be sharpened and the 5th needs to be naturalised)?

At first I was going to just write a 7 with a natural underneath and a flat below the natural, but it kinda doesn't look right, I think. Should I write in the 5 and 3 as well?

Maybe I've not understood, but if you are in the key of G minor then the dominant 7th won't start on A.

I take it there is a modulation to the dominant i.e D major/minor so thereore a secondary dominant

I would write it as

7
natural 5
sharp 3

Yeah, the key signature is g minor but the key of the moment is d minor. I think the way you suggested is probably the safest bet.

The number "3" is not needed in figured bass notation, just the sharp sign.

So you would do it like this:

7
5 natural
sharp

?

Yes.