Roam semi-nude when drunk, giving slight offence (12)
I believe the answer is:
misdemeanour
'slight offence' is the definition.
'misdemeanour' can be an answer for 'offence' (synonyms). I'm not certain of the 'slight' bit.
'roam semi-nude when drunk' is the wordplay.
'when drunk' indicates anagramming the letters (a drunken or disorderly form of the letters).
'roam'+'semi'+'nude'='roamseminude'
'roamseminude' is an anagram of 'MISDEMEANOUR'.
'giving' is the link.
Can you help me to learn more?
(Other definitions for misdemeanour that I've seen before include "Minor wrongdoing" , "Minor offence" , "Minor violation" .)