Slight resistance in cabal backing city (10)
I believe the answer is:
fractional
'slight' is the definition.
'resistance in cabal backing city' is the wordplay.
'resistance' becomes 'r' (abbreviation).
'in' indicates putting letters inside.
'cabal' becomes 'faction' ('faction' can be a synonym of 'cabal'**).
'backing' shows that the letters should be reversed in order.
'city' becomes 'la' (Los Angeles).
'la' reversed gives 'al'.
'r' placed within 'faction' is 'fraction'.
'fraction'+'al'='FRACTIONAL'
(Another definition for fractional that I've seen is " Very little".)