A little bit of male offensiveness gets Charlie arrested (7)
I believe the answer is:
modicum
'a little bit' is the definition.
(modicum means a very small amount)
'male offensiveness gets charlie arrested' is the wordplay.
'male' becomes 'm' (common abbreviation).
'offensiveness' becomes 'odium' (odium is disgust or offensiveness).
'gets' is a charade indicator (letters next to each other).
'charlie' becomes 'c' (phonetic alphabet: alpha, bravo, charlie etc.).
'arrested' means one lot of letters goes inside another (arrest can mean to hold or imprison).
'm'+'odium'='modium'
'modium' placed around 'c' is 'MODICUM'.
'of' is the link.
(Other definitions for modicum that I've seen before include "Tad" , "touch" , "Mum, I cod about a small amount" , "I cod Mum into providing a small quantity" , "Little bit" .)