Our older cats always taught the new pups manners, in the way of putting stripes across their noses. Usually just took once.
The other thing, is to have Willow on a leash, and teach her to do a down/stay when the kitty is in the room, at least until they are used to each other and have come to an understanding. We have a zero tolerance of kitty chasing here.
Brenna came to us as an adult rescue who really wanted to catch our kitties. The first time she was allowed off-leash in the house (after we'd worked with her and
thought she understood), she took off after one of the cats, chased it through the diningroom...managed to slide into the base of the heavy oak dining table and throw it against the wall.....proceeded into the livingroom, rearranging the sofa and coffee table in the process...throw carpets were "thrown" in every direction, and the cat headed for mom. Mom caught Brenna and Brenna did a LONG down/stay. It took a while, but she's got the idea now.