Second home acquired by mum (6)
I believe the answer is:
minute
'second' is the definition.
('minute' can be a synonym of 'second')
'home acquired by mum' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'acquired by' indicates putting letters inside.
'mum' becomes 'mute' (to keep mum is to remain silent).
'in' put within 'mute' is 'MINUTE'.
(Other definitions for minute that I've seen before include "60 seconds; tiny" , "Immeasurably small" , "official memorandum" , "Sixty seconds" , "Brief note" .)