Arab in rush to be admitted to hospital (7)
I believe the answer is:
saracen
'arab' is the definition.
(Saracen is an example)
'rush to be admitted to hospital' is the wordplay.
'rush' becomes 'race' ('race' can be a synonym of 'rush').
'to be admitted to' indicates putting letters inside.
'hospital' becomes 'san' (I've seen this in other clues).
'race' inserted within 'san' is 'SARACEN'.
'in' acts as a link.
(Other definitions for saracen that I've seen before include "Muslim opposing the Crusades" , "Opponent of the Crusaders" , "Crusader's foe" , "Old Arab" , "Arab (opposing the Crusaders)" .)