Baronet, no bachelor, rising as a singer (5)
I believe the answer is:
tenor
'a singer' is the definition.
(I know that tenor is a type of singer)
'baronet no bachelor rising' is the wordplay.
'no' is a deletion indicator.
'bachelor' becomes 'BA' (abbreviation for Bachelor of Arts degree).
'rising' is a reversal indicator (letters written upwards in a down clue).
'baronet' with 'ba' removed is 'ronet'.
'ronet' reversed gives 'TENOR'.
'as' is the link.
(Other definitions for tenor that I've seen before include "High voice - low bell" , "Male voice (one of three?)" , "One singing" , "Male singing voice of high pitch" , "Placido Domingo, say" .)