Get right into Mum's gangster cheese! (10)
I believe the answer is:
mascarpone
'cheese' is the definition.
(I've seen this before)
'get right into mum's gangster' is the wordplay.
'get right' becomes 'r' (I've seen this in other clues).
'into' is an insertion indicator.
'mum's' becomes 'ma's' (both can mean mother).
'gangster' becomes 'capone' (Al Capone).
'mas'+'capone'='mascapone'
'r' going into 'mascapone' is 'MASCARPONE'.
(Other definitions for mascarpone that I've seen before include "Soft Italian cheese" , "Italian cream cheese" .)