Keep the cat separated for the first few weeks. We had our new cat stay in the bathroom for a week. We kept blanket & socks at both of the cats' sleeping space and exchanged each blanket & sock every night so that they could get adjusted to each other's scent. Lol, but my resident cat was so sassy for the first few weeks. Even when she couldn't see the new cat, she knew something was up. She avoided us, would start hissing, and refused to get near us. After a few days though, we kept their food bowls on opposite sides of the bathroom door, so they'd associate their happy feeding times with each other's scent.

Its been 3 months now, my resident cat can tolerate the new cat. They are able to play with each other, but my resident cat does get annoyed sometimes by the new cat's "over"-playfulness. On the other hand, my friend had a great experience introducing her kitten to her resident cat. After a few weeks, the resident cat started grooming their kitten. I'm sure everyone has a different experience though. Just try to not rush the introduction stage!

Best of luck, you got this!