Pretty straightforward but needs managing. It's an issue for sighthounds, mainly because while many breeds chase cats, pointies are quick enough to catch them.
Firstly, make sure your garden is as inaccessible as possible for visiting cats, and do everything you can to discourage cats from entering. We use a water pistol if we see any and most of our neighbourhood cats now give us a wide berth.
On neighbourhood walks, in areas where there will be cats around, don't use a flexi lead, use good quality, well fitted lead and collar, and consider using a muzzle. If he/she is a sighthound, they will probably be comfortable with/used to these anyway.
On walks where you can safely go offlead e.g. beach, park well away from cats, open countryside, it will be safer - you may wish to retain muzzle for peace of mind.
Most sighthound charities will have info on local places that are securely fenced for safe offlead play/running, and there are private ones available as well.
Bear in mind that the RSPCA prosecuted a greyhound owner under the Animal Welfare Act whose dog was on the lead, walking near their home, and a cat jumped out of a hedge in front of them. The dog attacked the cat, and the RSPCA took the view (which the court agreed with) that this was preventable e.g. by muzzling.
I would strongly recommend booking yourself onto one of Trevor Cooper's DogLaw seminars (as I would for any dog owner) as he goes into detail on a number of key legal issues. His website lists forthcoming events.
And of course (and again, good advice for all dog owners) make sure you have adequete 3rd party insurance, and check if yr insurance offers any legal advice cover - some household policies do, and that might be useful.