Composer taking taxi back to hospital (4)
I believe the answer is:
bach
'composer' is the definition.
(Johann Sebastian Bach)
'taxi back to hospital' is the wordplay.
'taxi' becomes 'cab' (synonyms).
'back' says the letters should be written backwards.
'to hospital' becomes 'H' (abbreviation for hospital on maps).
'cab' in reverse letter order is 'bac'.
'bac'+'h'='BACH'
'taking' is the link.
(Other definitions for bach that I've seen before include "Musical family" , "musician" , "German composer (affectionate to a Welshman?)" , "Name of composing family" , "Johann Sebastian . . . . , great composer (4)" .)