Son, popular, gives offence (3)
I believe the answer is:
sin
'offence' is the definition.
(a sin is an offence or transgression)
'son popular' is the wordplay.
'son' becomes 's' (genealogical abbreviation for son).
'popular' becomes 'in' ('in' can mean trendy).
's'+'in'='SIN'
'gives' acts as a link.
(Other definitions for sin that I've seen before include "Immorality" , "Serious offence" , "Fall from grace" , "Immoral act" , "Evil" .)