Nearly go down for offence (3)
I believe the answer is:
sin
'offence' is the definition.
(thesaurus)
'nearly go down' is the wordplay.
'nearly' means to remove the last letter.
'go down' becomes 'sink' (sinking is a kind of going down).
'sink' with its final letter removed is 'SIN'.
'for' is the link.
(Other definitions for sin that I've seen before include "Wickedness" , "Serious offence" , "Mortal error" , "Immoral act" , "Immorality" .)