Agitation no end with affair that is oppressive (8)
I believe the answer is:
stifling
'oppressive' is the definition.
(thesaurus)
'agitation no end with affair' is the wordplay.
'agitation' becomes 'stir' (stir is a kind of agitation).
'no end' means to remove the last letter.
'with' means one lot of letters go next to another.
'affair' becomes 'fling' (I have seen 'Brief affair' mean 'fling' so perhaps 'affair' could also mean 'fling').
'stir' with its final letter removed is 'sti'.
'sti'+'fling'='STIFLING'
'that is' is the link.
(Other definitions for stifling that I've seen before include "Unpleasantly hot or airless" , "Flings it in suffocating manner" , "really hot" , "close?" , "Oppressively hot and airless" .)