Stay to suspend a fight (4,5)
I believe the answer is:
hang about
'stay' is the definition.
(I've seen this before)
'suspend a fight' is the wordplay.
'suspend' becomes 'hang' (I've seen this before).
'fight' becomes 'bout' ('bout' can be a synonym of 'fight').
'hang'+'a'+'bout'='HANG ABOUT'
'to' is the link.
(Other definitions for hang about that I've seen before include "Stay" , "Loiter or linger 9 in suspense?" , "Wait a minute! Stick around!" .)