Girl’s name for a doctor and monarch (5)
I believe the answer is:
amber
'girl's name' is the definition.
'a doctor and monarch' is the wordplay.
'doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus**).
'and' is a charade indicator (letters next to each other).
'monarch' becomes 'er' (abbreviation for Elizabeth Regina).
'a'+'mb'+'er'='AMBER'
'for' is the link.
(Other definitions for amber that I've seen before include "Yellow, translucent fossil resin" , "first light" , ""Stop" traffic light" , "Light colour between red and green" , "Traffic-light colour" .)