Native American husband leaves quickly (5)
I believe the answer is:
apace
'quickly' is the definition.
(I know that quickly can be written as apace)
'native american husband leaves' is the wordplay.
'native american' becomes 'apache' (group of Native American tribes).
'husband' becomes 'h' (abbreviation).
'leaves' indicates named letters should be taken away.
'apache' with 'h' taken out is 'APACE'.
(Other definitions for apace that I've seen before include "Swiftly, quickly" , "At a rapid rate" , "flat out" , "Quick" , "What's quickly" .)