Quick, the doctor's in the river! (6)
I believe the answer is:
nimble
'quick' is the definition.
('nimble' can be a synonym of 'quick')
'the doctor's in the river' is the wordplay.
'the doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus).
'in the' means one lot of letters goes inside another.
'river' becomes 'nile' (Nile is an example).
'mb' placed inside 'nile' is 'NIMBLE'.
(Other definitions for nimble that I've seen before include "Quick on the feet" , "Agile, sprightly" , "Moving quickly and lightly" , "Quick moving" , "Swift, active" .)