End of chase, heading off people on horses — we get down from them (6)
I believe the answer is:
eiders
'we get down from them' is the definition.
(ducks that provide down feathers)
'end of chase heading off people on horses' is the wordplay.
'end of' indicates one should take the final letters.
'heading off' means to remove the first letter.
'people on horses' becomes 'riders' (horse riders).
The final letter of 'chase' is 'e'.
'riders' with its first letter removed is 'iders'.
'e'+'iders'='EIDERS'
(Another definition for eiders that I've seen is " Ducks with fine soft down".)