Native American horse stopping quickly (6)
I believe the answer is:
apache
'native american' is the definition.
(I've seen this before)
'horse stopping quickly' is the wordplay.
'horse' becomes 'h' ('H' can be a synonym of 'horse').
'stopping' means one lot of letters goes inside another (stopping can mean blocking a gap).
'quickly' becomes 'apace' ('apace' can be a synonym of 'quickly').
'h' inserted into 'apace' is 'APACHE'.
(Other definitions for apache that I've seen before include "Parisian gangster" , "Fierce Indian of American SW, or Paris ruffian" , "US native" , "Hooligan in Paris" , "American speech" .)