It got so complicated that the (never made) TOS-era New Voyages fan film adaptation of the (also unmade) Enterprise season 5 Kzinti episode "Kilkenny Cats" chose to swap the Kzinti for the Kythari (sp?), a feloid race from an officially published Trek short story.I do not know whether it is legally possible to depict Kzinti in new Star Trek productions.
One one hand, the Kzinti were created by Larry Niven for his "known space" series which is a totally different ficitonal setting than the Star Trek setting and are owned by Larry Niven.
On the other hand, Niven permitted Kzinti to appear in the TAS episode "The Slaver Weapon" and wrote the episode himself based on his story "The Soft Weapon", thus letting his Kzinti, or some sort of parallel universe version of them, become part of any fictional universe which includes the TAS episode "The Slaver Weapon.
So I suspect that lawyers will be consulted before any Kzinti appear in any new Star Trek productions.
90's TNG novel The Captain's Honor features the M'dok, who were originally meant to be Kzinti.
Picard showrunner Michael Chabon sought Larry Niven's permission for the Kzinti namedrop there. But a namedrop is one thing, featuring them is another.