Confuse teams beforehand demonstrating old-fashioned way of riding (10)
I believe the answer is:
sidesaddle
'way of riding' is the definition.
(I've seen this before)
'confuse teams beforehand' is the wordplay.
'confuse' becomes 'addle' (addling is a kind of confusing).
'teams' becomes 'sides' (eg football sides).
'beforehand' means one lot of letters go next to another.
'addle' put after 'sides' is 'SIDESADDLE'.
'demonstrating old-fashioned' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for sidesaddle that I've seen before include "mounting style" , "way of riding" .)