Nearly having a fit (5)
I believe the answer is:
about
'nearly' is the definition.
(I've seen this before)
'a fit' is the wordplay.
'fit' becomes 'bout' (I've seen this in other clues).
'a'+'bout'='ABOUT'
'having' acts as a link.
(Other definitions for about that I've seen before include "in the offing?" , "Concerning; roughly" , "nearby" , "Encompassing" , "In conection with, all around" .)