Conures are tough new world parrots and have a hefty bite. Inevitably your bird and cat will be alone, in the same room without boundaries (worst case scenario) so good on you for wanting to introduce your FAMILY MEMBERS to each other so everyone can be civil & well behaved

Having said that - I don't know cats. However, I've introduced my dog and family dogs to my parrots (even my budgies) and now everyone gets along. Even the chihuahua (who will kill sparrows and mice) doesn't even flinch when the budgies are on the floor hanging' out.
Try bird tricks on youtube to get your answer and please enjoy all the free flying and engage not cage channels. Adventures of Roku, Mikey the Macaw, Parrot Wizard, and Marlene Mc'Cohen.
You know your cat best, have you introduced her to any other animals? You can gauge her response based on previous encounters with smaller animals.
Then, you'll have to gauge the bird's response with your cat... please bond well with your new parrot - it'll mean just about everything moving forward.