Native American evicts husband quickly (5)
I believe the answer is:
apace
'quickly' is the definition.
(I know that quickly can be written as apace)
'native american evicts husband' is the wordplay.
'native american' becomes 'Apache' (group of Native American tribes).
'evicts' is a deletion indicator.
'husband' becomes 'h' (abbreviation).
'apache' with 'h' taken out is 'APACE'.
(Other definitions for apace that I've seen before include "(Move on) swiftly" , "At a rapid rate" , "What's quickly" , "Swiftly, quickly" , "fast" .)