Director, born in Kent, first to have better managed a good hospital (7,7)

'director' is the definition.
(Kenneth Branagh is an actor and director)

'born in kent first to have better managed a good hospital' is the wordplay.
I cannot really understand how this works, but
'born' could be 'ne' ('born' in French - used to indicate a birth name) and 'ne' is found within the answer.
'first' could be 'a' (first letter of the alphabet) and 'a' is located in the answer.
'a' is found in the answer.
'good' could be 'g' (abbreviation) and 'g' is found within the answer.
'hospital' could be 'h' (abbreviation for hospital on maps) and 'h' is present in the answer.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?