Rarely means "seldom," "infrequently," "not often": "She rarely goes to the movies." The phrase "rarely ever" is wordy, unidiomatic, and illogical. Instead of saying "She rarely ever sings," say "She rarely sings" or "She hardly ever sings" or "She sings rarely, if ever" or "She sings rarely or never."
Dictionary of problem words and expressions. Harry Shaw. 1975.