Nearly having a fight (5)
I believe the answer is:
about
'nearly' is the definition.
(I've seen this before)
'a fight' is the wordplay.
'fight' becomes 'bout' (synonyms).
'a'+'bout'='ABOUT'
'having' acts as a link.
(Other definitions for about that I've seen before include "Moving" , "Concerning or in neighbourhood" , "Encompassing" , "nearby" , "Concerning or around" .)