Singer backed by company offering headgear (7)
I believe the answer is:
coronet
'headgear' is the definition.
(coronet is a kind of headgear)
'singer backed by company' is the wordplay.
'singer' becomes 'tenor' (tenor is a kind of singer**).
'backed' is a reversal indicator.
'by' says to put letters next to each other.
'company' becomes 'co' (abbreviation).
'tenor' back-to-front is 'ronet'.
'ronet' put after 'co' is 'CORONET'.
'offering' is the link.
(Other definitions for coronet that I've seen before include "Sub-lieutenant" , "in the band" , "badge of rank" , "Peer's headgear" , "brass embellishment" .)