Circuit of a doctor in the island (5)
I believe the answer is:
ambit
'circuit' is the definition.
(I've seen this in another clue)
'doctor in the island' is the wordplay.
'doctor' becomes 'mb' (Bachelor of Medicine).
'in the' is an insertion indicator.
'island' becomes 'ait' (term for a small island).
'mb' placed into 'ait' is 'AMBIT'.
'of a' acts as a link.
(Other definitions for ambit that I've seen before include "round" , "Circuit, compass" , "Scope or circuit" , "Scope or confines" , "Range - surroundings" .)