Sport!

There is real life precendence.

Many sports in real life derive from military skills - martial arts, kendo, fencing (sort of), archery, some horse sports and so on. Some of these sports were at least in part invented so that the warrior caste could keep their skills sharp in between wars.

Also, look up the Haka, a traditional war dance performed by some Rugby teams at internationals. This indicates that for some, Rugby has replaced tribal warfare as a means to demonstrate prowess and the warrior spirit etc.

So, for your story, create a sport that can be abstract to bloodthirsty as needs be. This means that the warrior caste are useful as entertainment for the other castes, and can serve as a proxy for any residual bloodlust left over.

You could also have it that the political class have created this sport specifically to train warriors for a possible future war in secret, a bit like Ender's Game or some such.

Sport!

There are real-life precedents.

Many sports in real life derive from military skills - martial arts, kendo, fencing (sort of), archery, some horse sports, and so on. Some of these sports were at least in part invented so that the warrior caste could keep their skills sharp in between wars.

Also, look up the Haka, a traditional war dance performed by some rugby teams at internationals. This indicates that for some, rugby has replaced tribal warfare as a means to demonstrate prowess and the warrior spirit etc.

So, for your story, create a sport that can be abstract to bloodthirsty as needs be. This means that the warrior caste are useful as entertainment for the other castes, and can serve as a proxy for any residual bloodlust left over.

You could also have it that the political class have created this sport specifically to train warriors for a possible future war in secret, a bit like Ender's Game or some such.