Ready to take part on horseback, on account of Italian (2,3,2)
I believe the answer is:
up for it
'ready to take part' is the definition.
(I've seen this before)
'on horseback on account of italian' is the wordplay.
'on horseback' becomes 'up' (up can mean up on a horse).
'on account of' becomes 'for' (both can mean 'because' or 'as a result of').
'italian' becomes 'it' (abbreviation for Italian).
'up'+'for'+'it'='UP FOR IT'
(Other definitions for up for it that I've seen before include "Ready to take part" , "Enthusiastic" , "Game" .)