Prominent Florentine family shortly finding doctor (5)
I believe the answer is:
medic
'doctor' is the definition.
(doctor is a type of medic)
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for medic that I've seen before include "He may offer treatment" , "Eg, doctor" , "Health worker" , "What was Basutoland" , "Physician (informal)" .)