Native American leaving hospital fast (5)
I believe the answer is:
apace
'fast' is the definition.
(apace can mean quickly)
'native american leaving hospital' is the wordplay.
'native american' becomes 'apache' (group of Native American tribes).
'leaving' suggests deleting specific letters.
'hospital' becomes 'h' (abbreviation for hospital on maps).
'apache' with 'h' removed is 'APACE'.
(Other definitions for apace that I've seen before include "Swiftly, quickly" , "At a rapid rate" , "flat out" , "Quick" , "fast" .)