One synonym for the phrase "primp up" is "groom." This term refers to the act of tidying up one's appearance and feeling confident in one's presentation. Another synonym is "preen," which specifically refers to the act of tidying up feathers or fur in the animal kingdom. "Smarten up" is another phrase that can be used to describe the act of improving one's appearance, suggesting that a person is looking to present themselves as more intelligent or sophisticated. "Spruce up" is yet another synonym, implying that a person is giving their appearance a polished, refined look through attention to small details. Overall, there are many different phrases that can be used as synonyms for the phrase "primp up".