Mother backing our love affair (5)
I believe the answer is:
amour
'love affair' is the definition.
(I've seen this before)
'mother backing our' is the wordplay.
'mother' becomes 'ma' (ma can mean mother).
'backing' says the letters should be written backwards.
'ma' reversed gives 'am'.
'am'+'our'='AMOUR'
(Other definitions for amour that I've seen before include "(Secret) lover" , "A secret love affair in France" , "Fling" , "Love affair, perhaps secret" , "20 [AFFAIR]" .)