Service nevertheless supported by Northern government (8)
I believe the answer is:
evensong
'service' is the definition.
(thesaurus)
'nevertheless supported by northern government' is the wordplay.
'nevertheless' becomes 'evenso' ('even so' can be a synonym of 'nevertheless').
'supported by' is a charade indicator (letters next to each other) (letters go below - in down clue).
'northern' becomes 'n' (abbreviation e.g. N. Ireland).
'government' becomes 'g'.
'evenso'+'n'+'g'='EVENSONG'
(Other definitions for evensong that I've seen before include "6 [SERVICE] ?" , "Church service late in the day" , "Anglican service" , "... Prayers" , "Religious service" .)