Pain has one going round hospital (4)
I believe the answer is:
ache
'pain' is the definition.
(ache is a kind of pain)
'one going round hospital' is the wordplay.
'one' becomes 'ace' (synonyms).
'going round' means one lot of letters goes inside another.
'hospital' becomes 'h'.
'ace' placed around 'h' is 'ACHE'.
'has' is the link.
(Other definitions for ache that I've seen before include "yearning" , "Feel sore" , "Play up" , "Nagging pain" , "suffering" .)