Doctor possibly fit to be a tenor (5)
I believe the answer is:
drift
'a tenor' is the definition.
(drift is a kind of tenor)
'doctor possibly fit' is the wordplay.
'doctor' becomes 'dr' (synonyms).
'possibly' is an anagram indicator.
'fit' with letters rearranged gives 'ift'.
'dr'+'ift'='DRIFT'
'to be' acts as a link.
(Other definitions for drift that I've seen before include "See 8" , "Trend; meaning" , "Move casually or aimlessly" , "Import" , "Snow heaped up by wind" .)