A1 family starting to get turned over by the mob (5)
I believe the answer is:
mafia
'the mob' is the definition.
(I know that Mafia is a type of mob)
'a1 family starting to get turned over' is the wordplay.
'am' becomes 'a'.
'starting' suggests taking the first letters.
'to get' is a charade indicator (letters next to each other).
'turned' becomes 'mia' (I can't justify this - if you can you should give a lot more credence to this answer).
'over' indicates putting letters inside.
The initial letter of 'family' is 'f'.
'a'+'f'='af'
'af' placed within 'mia' is 'MAFIA'.
'by' acts as a link.
Can you help me to learn more?
(Other definitions for mafia that I've seen before include "Sicilian criminal organisation" , "Sicilian criminals" , "Criminal organisation also known as Cosa Nostra" , "Criminal society" , "Sicilian secret society" .)