A fight with mug brings change of attitude (5-4)
I believe the answer is:
about face
'change of attitude' is the definition.
(I've seen this before)
'a fight with mug' is the wordplay.
'fight' becomes 'bout' (as in a bout in boxing).
'with' says to put letters next to each other.
'mug' becomes 'face' (I've seen this in another clue).
'a'+'bout'+'face'='ABOUT-FACE'
'brings' acts as a link.
(Other definitions for about face that I've seen before include "180 degree turn" , "U-turn" , "retreat" , "turnaround" , "Where a babe might get her food" .)