The palate was the roof of the mouth in Humans and other mammals, often more generally referring to the sense of taste.
In 2151, Elizabeth Cutler told Ethan Novakovich one probably needed a better palate than he had to appreciate Vulcan cuisine. (ENT: "Strange New World")
In 2267, Trelane invited an USS Enterprise landing party to eat with him since they had "victuals to delight the palate and brave company to delight the mind." (TOS: "The Squire of Gothos")
In 2367, Robert Picard told his brother he had drunk to much synthehol, which had ruined his palate. (TNG: "Family")
In 2368, Data informed Timothy that he couldn't taste, but analyze food and draw conclusions about its effect on the Human palate. (TNG: "Hero Worship")
When Kor was busy with two dabo girls in Quark's in 2370, he lamented he had to choose between perfection (the girls) and palate (a drink). (DS9: "Blood Oath")
In 2375, Tomin intended to broaden his palate while aboard the USS Voyager. (VOY: "Someone to Watch Over Me")
In 2377, when Seven of Nine cooked for the crew of the Voyager, Captain Janeway remarked she knew of Seven expanding her palate, but not that she had become a gourmet cook. (VOY: "The Void")