Mock mum in the morning (4)
I believe the answer is:
sham
'mock' is the definition.
(both can mean fake)
'mum in the morning' is the wordplay.
'mum' becomes 'sh' (both can be used to tell someone to be quiet).
'in the morning' becomes 'am' (short for ante meridiem - before noon).
'sh'+'am'='SHAM'
(Other definitions for sham that I've seen before include "imitation" , "Pretense; bogus" , "Phoney, bogus" , "charade" , "Pretence; bogus, false" .)