Quick -- doctor's in river! (6)
I believe the answer is:
nimble
'quick' is the definition.
('nimble' can be a synonym of 'quick')
'doctor's in river' is the wordplay.
'doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus).
'in' is an insertion indicator.
'river' becomes 'nile' (Nile is an example**).
'mb' placed inside 'nile' is 'NIMBLE'.
(Other definitions for nimble that I've seen before include "Swift, active" , "Quick on the feet" , "'Jack be ......, Jack be quick' (6)." , "Fast; light in movement" , "Quick moving" .)