A partnership was a formal arrangement by two or more parties to manage and operate a business and share its profits.
In 2370, Martus Mazur promised Rom a one quarter partnership in his business, Club Martus. When Rom dared Quark to make him a better offer to get him to stay with Quark's, Quark found the idea of having a bidding war over Rom to be laughable. (DS9: "Rivals")