The case is a female, at hospital (6)
I believe the answer is:
sheath
'the case' is the definition.
(synonyms)
'female at hospital' is the wordplay.
'female' becomes 'she' (I've seen this before).
'hospital' becomes 'h'.
'she'+'at'+'h'='SHEATH'
'is a' is the link.
(Other definitions for sheath that I've seen before include "Cover for a sword" , "Cover for a knife" , "Cover protecting" , "Close fitting dress" , "Covering for blade" .)