One might nick food rejected by the French right (7)
I believe the answer is:
burglar
'one might nick' is the definition.
(I know that burglars often steal)
'food rejected by the french right' is the wordplay.
'food' becomes 'grub' (grub can informally mean food).
'rejected' says the letters should be written backwards.
'by' means one lot of letters go next to another.
'the french' becomes 'la' (one of the French words for 'the').
'right' becomes 'r' (abbreviation).
'grub' written backwards gives 'burg'.
'burg'+'la'+'r'='BURGLAR'
(Other definitions for burglar that I've seen before include "Intruder with intent to steal" , "A criminal on one's premises" , "Housebreaker" , "Breaker and enterer?" , "House-violating thief" .)