lets say my opponent has a team-up, say vu and checkmate. On the field they only have a checkmate character.

Turn 7 they recruit deathstroke, can I chain to the recruit, blow up the team-up and make them unable to recruit deathstroke?

Thing is, he already has recruited Deathstroke, by placing him on the chain; recruiting a character is equivalent to playing an effect. You can get rid of his team-up before Deathstroke comes into play, no doubt, but he's already met the Loyalty requirement.

In the same way, you can't use Null Time Zone to negate effects that are already on the chain; they're waiting to resolve, but they've definitely been played.