Engagement risks him becoming distraught (8)
I believe the answer is:
skirmish
'engagement' is the definition.
(I have seen 'Short engagement' mean 'skirmish' so perhaps 'engagement' could also mean 'skirmish')
'risks him becoming distraught' is the wordplay.
'becoming distraught' is an anagram indicator.
'risks'+'him'='riskshim'
'riskshim' anagrammed gives 'SKIRMISH'.
(Other definitions for skirmish that I've seen before include "Short conflict" , "Minor short-term fight" , "Minor fight or conflict" , "Scrap" , "Minor engagement -- his smirk (anag)" .)