Public official never admits to being promoted (6)
I believe the answer is:
notary
'public official' is the definition.
(I've seen this before)
'never admits to being promoted' is the wordplay.
'never' becomes 'nary' (I've seen this in other clues).
'admits' is an insertion indicator.
'being promoted' is a reversal indicator (going up, in a down clue).
'to' reversed gives 'ot'.
'nary' enclosing 'ot' is 'NOTARY'.
(Other definitions for notary that I've seen before include "Official working on legal documents" , "Official authorised to witness signing of documents" , "A public one certifies documents" , "Certifier of deeds etc." , "Public official, usually a solicitor" .)