Expert outside hospital in pain (4)
I believe the answer is:
ache
'pain' is the definition.
(ache is a kind of pain)
'expert outside hospital' is the wordplay.
'expert' becomes 'ace' (ace can informally mean very good).
'outside' means one lot of letters goes inside another.
'hospital' becomes 'H' (abbreviation for hospital).
'ace' going around 'h' is 'ACHE'.
'in' acts as a link.
(Other definitions for ache that I've seen before include "burn" , "Hurt; yearn" , "yearning" , "Pine" , "Persistent dull pain" .)