Native American leaving hotel swiftly (5)
I believe the answer is:
apace
'swiftly' is the definition.
(synonyms)
'native american leaving hotel' is the wordplay.
'native american' becomes 'apache' (group of Native American tribes).
'leaving' is a deletion indicator.
'hotel' becomes 'h' (phonetic alphabet: alpha, bravo, charlie etc.).
'apache' with 'h' taken out is 'APACE'.
(Other definitions for apace that I've seen before include "flat out" , "Quick" , "What's quickly" , "fast" , "(Move on) swiftly" .)