Tim Stamper is a great character, but....SPOILERS

He's in part three quite a bit.

Tim has a backstory with Urquhart as being his political cohort/friend/lackey for some years back. Probably more lackey than anything else. It's suggested that he has something of a 'hero-worship' attitude towards Urquhart, would do literally anything for him...but also has some underlying jealousy and resentment as well. It's also vaguely hinted that his feelings for Urquhart might be even something a little, shall we say, deeper than that.

I think he's made into more of an 'enforcer type' in the second series, so that what ultimately becomes of him makes more sense both on plot and emotional levels. We see Urquhart's attitude start to shift towards Tim, become more openly contemptuous of him, treating him more like a functionary than a friend. Partly that's also to suggest how Urquhart has begun to shut himself down emotionally towards everyone around him--his relationship with Sarah is obviously on a different level from the one he had with Mattie as well, more openly cold-blooded and purely pragmatic. That Tim has probably always considered himself to be Urquhart's closest friend just serves to make his subsequent treatment of him cause Tim to become even more resentful.

It's one of the points I like best about the series, the complexities of the relationships between the characters, that are more often hinted at than spelled out plainly to the audience.