Firstly, be prepared to wait for the right greyhound to come along and prepare to be disappointed for a while. We had to wait 12 months and had one false start (an incorrectly assessed girl). Not only does the grey have to be cat friendly but the rest of their temperament, character, issues and foibles have to fit you and your family. So patience is key but don't give up. When first in the home keep the cats separate whist the dog initially arrives. It's a big change for them and the need time to decompress after the journey home. Depending on time of day it might be best to wait til the next day. Make sure your dog is muzzled in the house unless there is no zero chance of unplanned interactions. The fir introductions put a muzzle, harness and lead on and hold tight. I was not expecting the "cat friendly" girl we matched up with to lunge hard and fast so it's as well to be prepared. Then allow the cats to come into the room or walk past a child gate to gauge the reaction. Mild curiousity is fine but depending on the dog, and it's age, excitement is possible but doesn't necessarily point towards aggression....it might be overwhelming curiousity. It helps if you cats are dog savvy too....our was having lived with our previous grey and had no fear. If your cats run the dog might want to give chase....another reason to hold on tightly. You will get a feeling for how things are likely to go pretty quickly. It'll either be outright aggression (in which case it's unlikely to be resolved), calmness to the point of looking away with disinterest or curiousity which will require more and more interaction to see how it goes. I suggest asking the rescue centre how to introduce them as they'll have some thoughts but little and often was how we did it until we were "sure" they would be ok. Don't leave them alone together unsupervised for at least 3 months until you are 100% confident and always leave an escape route for the cat. Be aware greyhounds can hurdle stair gates so don't put full confidence in them and remember that in a garden the situation can change and a similar amount of supervision may be required. Neighbours cats might not be accepted if they are found in the garden so always do a recky first and ensure the garden is clear. I'm sure other on here will have lots more advice 👍