An art critic was someone who judged artwork.
In 2366, while mourning the apparent loss of Data, Geordi La Forge recalled that Data was a critic of his own paintings, after Wesley Crusher mentioned that the android never thought a particular painting was quite finished. (TNG: "The Most Toys")
In 2375, Norvo Tigan destroyed several pieces of his own artwork. When Ezri Dax expressed her surprise at his actions, he explained, "When I get drunk, I become an art critic." (DS9: "Prodigal Daughter")