Second person's no good offspring (5)
I believe the answer is:
young
'offspring' is the definition.
('young' can be a synonym of 'offspring')
'second person's no good' is the wordplay.
'second person' becomes 'you' (I've seen this before).
'no' becomes 'n' (common abbreviation).
'good' becomes 'g' (abbreviation).
'you'+'n'+'g'='YOUNG'
(Other definitions for young that I've seen before include "Newly-developed" , "Offspring; immature" , "issue" , "Youthful" , "Born recently" .)