Policeman left girl: that’s the problem (7)
I believe the answer is:
dilemma
'the problem' is the definition.
(a dilemma is a problem)
'policeman left girl' is the wordplay.
'policeman' becomes 'di' (abbreviation for Detective Inspector).
'left' becomes 'L' (common abbreviation).
'girl' becomes 'emma' (girl's name).
'di'+'l'+'emma'='DILEMMA'
'that's' acts as a link.
(Other definitions for dilemma that I've seen before include "I'm lamed - it's a puzzle" , "tricky position" , "Difficult decision" , "Problem (with horns?)" , "Catch-22" .)