Crossword Genius

Medic gives drip to hesitating chauffeur (6)

Ross

I believe the answer is:

driver

I'm a little stuck... Click here to teach me more about this clue!

'chauffeur' is the definition.
(I know that chauffeur can be written as driver)

'medic gives drip to hesitating' is the wordplay.
I cannot quite understand how this works, but
'medic' could be 'dr' (doctor) and 'dr' is found within the answer.
'drip' could be 'iv' (intravenous drip) and 'iv' is located in the answer.
'hesitating' could be 'er' and 'er' is present in the answer.
No letters remain.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for driver that I've seen before include "See 1 down" , "Golf-club for a motorist" , "Operator of a motor vehicle" , "chauffeuse" , "Golf club for long shots" .)

I've seen this clue in The Mirror.
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