This - it's do-able.
The dog will learn that if he leaves the cat alone, he will get more freedom. (1). Contact a GOOD dog behaviourist - I say GOOD because there are a lot of useless charlatans out there - get one with really good reviews, and make sure they are prepared to come to your home to see the dog. Seeing them in their clinic is no good.
If your dog isn't neutered, get him/her neutered now.
Is your dog left alone most of the day? If so, he/she is bored witless and is using the cat to relieve that awful boredom. He is playing - but that doesn't mean that he couldn't badly hurt, or even kill the cat because HE IS A PUPPY AND DOESN'T KNOW HOW TO RESTRAIN HIMSELF. (2) You have to teach him this, but you also need to keep him well exercised and mentally stimulated so that he fits it easier to keep calm next to the cat.
Shouting at the dog will further over-excite him, or frighten him, depending on his temperament. Keep calm. A firm "No" and them put him into an indoor kennel (3)/ another room for five minutes every time he tries to chase - he'll soon learn that chasing means he is deprived of your company.
Lots of dogs from abroad have huge problems. Most have lived on the streets and had to fight for every mouthful of food. They've learned to be wary of people because they usually get kicked, or stones thrown at them. They usually have had an horrific journey - often for three/ four days overland, then a sea journey, then another day overland, trapped in a dark airless van with maybe 20 other panicking, terrified dogs - all of which are defecating, urinating, vomiting - perhaps not much food or water (4). Unsurprisingly they can take a while to settle - and once settled, just like difficult children, when they begin to get their confidence they test the limits of what they're allowed to do.
Your dogs still young. With patience and training he has a good chance of setting - but you MUST protect the poor cat, especially as she has regarded the dog as her friend up until now, and won't know what's hit her!
Wishing you luck, because I, too, can't part with an animal once I've taken responsibility for it (and fallen in love with it).
(1). Most probably. Some dogs, usually terrier types, never learn to control that strong prey drive (Patterdales in particular are absolute buggers, IME, and some yorkies can be, too)
(2) Puppies in a litter are very rough with each other, but when one yelps, the other will stop nipping. Cats have different body language - and they don't yelp. The actions the cat takes (fleeing, spitting, lashing out with claws) are interpreted by the dog as an invitation to continue playing. And dogs love to chase - the cat runs away, the dog thinks she's saying "Chase me! This is fun!" The dog could easily hurt the cat - and the cat could easily blind the dog, and will if that's her only choice.
(3) If you haven't got one, get one. Normally I wouldn't recommend using it for "punishment" because it should be the dog's private space where he can come and go, but if you aren't there to supervise, or if you need him out of the way for a very short time, it's ideal. He will learn to associate it with being calm.
(4) I'm not trying to criticise the drivers etc - I think they do their very best, but it is impossible to keep animals properly clean in those conditions - for = upset bowels, plus water will get spilled, many will be too terrified to eat, or will vomit any food back up.