Pet problem? (5)
I believe the answer is:
peeve
'pet problem?' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for peeve that I've seen before include "Cause resentment" , "Vex" , "Cause annoyance" , "upset" , "Cause to be annoyed, irritated, or resentful" .)