19th.c cavalry in Ireland

[RobinSmith]

I have an ancestor, James Appleyard, who was in Cahir, Tipperary in 1823 and in Nottingham in 1827 for a short time and then in Worcestershire. I assume he was a soldier as he described himself on one occasion as trumpeter and on another as musician (daughter's Christening then wedding) and Cahir had a large cavalry barracks in the early 19th c. This is all I have to go on.
Are there any records, such as discharge papers, etc. in existence for this period?
I'd be grateful for any help.

Robin.