Skilful doctor beginning to operate in island (6)
I believe the answer is:
adroit
'skilful' is the definition.
(I've seen this before)
'doctor beginning to operate in island' is the wordplay.
'doctor' becomes 'Dr' (abbreviation).
'beginning to' says to take the initial letters.
'in' means one lot of letters goes inside another.
'island' becomes 'ait' (I've seen this before).
The initial letter of 'operate' is 'o'.
'dr'+'o'='dro'
'dro' inserted within 'ait' is 'ADROIT'.
(Other definitions for adroit that I've seen before include "Skilled" , "To raid (anag)" , "Clever, skilful" , "Dextrous" , "Apt" .)