Take half of horse-rider's accessories to mix things up? (4)
I believe the answer is:
stir
'mix things up?' is the definition.
(I've seen this in another clue)
'take half of horse-rider's accessories' is the wordplay.
'take' becomes 'cast' (casting is a kind of taking).
'half of' means to take half the letters.
'horse-rider's accessories' becomes 'ir' (I can't justify this - if you can you should give a lot more credence to this answer).
'cast' cut in half is 'st'.
'st'+'ir'='STIR'
'to' acts as a link.
Can you help me to learn more?
(Other definitions for stir that I've seen before include "Move around in a liquid" , "beat" , "Budge" , "Excitement" , "What keeps those inside" .)