Dishonest part of family in Genoa (5)
I believe the answer is:
lying
'dishonest' is the definition.
('lying' can be a synonym of 'dishonest')
'part of family in genoa' is the wordplay.
'part of' indicates the answer is hidden within the clue.
'LYING' is hidden within 'family in genoa'.
(Other definitions for lying that I've seen before include "possibly, to be mendacious" , "Deceit" , "Flat-out" , "Saying what is 23" , "not to be trusted?" .)