"The Sims 4's ownable vet clinic is available to players who buy the Cats and Dogs Expansion. This new feature borrows heavily from the Get to Work Doctor Career, as well as that DLC's Retail feature and Veterinarian Skill which ties in with the business ownership feature, but is not exclusively used for operating a clinic." Taken from
Carl's Sims 4 Guide
So, no, you dont need Get to work. you only need base game and Cats & Dogs. =3