Crook in US city with last of beer in mug (10)
I believe the answer is:
lawbreaker
'crook' is the definition.
(I know that lawbreaker is a type of crook)
'us city with last of beer in mug' is the wordplay.
'us city' becomes 'LA' (short for Los Angeles).
'with' becomes 'w' (short for with).
'last of' indicates one should take the final letters.
'in' means one lot of letters goes inside another.
'mug' becomes 'beaker' (I've seen this before).
The last letter of 'beer' is 'r'.
'r' put within 'beaker' is 'breaker'.
'la'+'w'+'breaker'='LAWBREAKER'
'in' is the link.
(Other definitions for lawbreaker that I've seen before include "Criminal" , "Villain" , "Delinquent" , "Perpetrator of crime" .)