Almost grieve after a love affair (5)
I believe the answer is:
amour
'love affair' is the definition.
(I've seen this before)
'almost grieve after a' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'grieve' becomes 'mourn' (mourning is a kind of grieving).
'after' says to put letters next to each other.
'mourn' with its final letter removed is 'mour'.
'mour' after 'a' is 'AMOUR'.
(Other definitions for amour that I've seen before include "Illicit love" , "Love affair, perhaps secret" , "Result of Cupid's darts" , "Romantic affair" , "Love affair - loved one" .)