Function involving clubs supported by bank — honestly (9)
I believe the answer is:
sincerely
'honestly' is the definition.
(synonyms)
'function involving clubs supported by bank' is the wordplay.
'function' becomes 'sin' (mathematical function).
'involving clubs' becomes 'ce' (I can't justify this - if you can you should give a lot more credence to this answer).
'supported by' is a charade indicator (letters next to each other) (in a down clue, some letters hold up others).
'bank' becomes 'rely' (to bank on is to rely on).
'sin'+'ce'+'rely'='SINCERELY'
(Other definitions for sincerely that I've seen before include "word often preceding a signature" , "How one may complete letter" , "Not showing any deceit" , "In good faith" , "Really" .)