Son at home gives offence (3)
I believe the answer is:
sin
'offence' is the definition.
(a sin is an offence or transgression)
'son at home' is the wordplay.
'son' becomes 's' (genealogical abbreviation for son).
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
's'+'in'='SIN'
'gives' acts as a link.
(Other definitions for sin that I've seen before include "Behave badly" , "Immoral act" , "'Transgression, mortal or venial (3)'" , "grave offence" , "Go astray" .)