Lives with girl? That’s the problem! (5)
I believe the answer is:
Here is my best explanation:
'the problem' is the definition.
'lives with girl?' is the subsidiary indication.
'lives' becomes 'is' ('be' can be a synonym of 'live').
'with' means one lot of letters go next to another.
'girl?' becomes 'sue' (**).
'that's' is the link.
(Other definitions for issue that I've seen before include "Matter of debate", "Important topic for debate", "Give out; children", "Debate topic; flow out", "Magazine", "one's children?", "Dispute", "One's offspring", "Concern" and "Subject for discussion; dish out".)