Native American wanting horse with speed (5)
I believe the answer is:
apace
'with speed' is the definition.
(I've seen this in another clue)
'native american wanting horse' is the wordplay.
'native american' becomes 'apache' (group of Native American tribes).
'wanting' suggests deleting specific letters (to want something can mean to lack it or need it).
'horse' becomes 'h' (synonyms).
'apache' with 'h' taken away is 'APACE'.
(Other definitions for apace that I've seen before include "flat out" , "fast" , "at high speed" , "Swiftly, quickly" , "Quick" .)