Doctor's Scotsman becoming first scientist (9)
I believe the answer is:
physicist
'scientist' is the definition.
(I know that physicist is a type of scientist)
'doctor's scotsman becoming first' is the wordplay.
I cannot quite see how this works, but
'first' could be 'ist' (ist resembles 1st) and 'ist' is present in the answer.
The remaining letters 'physic' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
(Other definitions for physicist that I've seen before include "To become a scientist, doctor gets a name change to the street" , "Expert in the science of matter and energy" , "One studying the nature of matter" .)