Tarr twice made the second round of the singles draw in a Grand Slam tournament. He defeated Mike De Palmer at the 1983 US Open and beat Christophe Roger-Vasselin at the 1984 Wimbledon Championships. His best performance on tour came in the 1984 Cincinnati Open, part of the Grand Prix Tennis Championship Series, where he reached the round of 16. He registered upset wins over Tim Mayotte at Queen's in 1982 and Henri Leconte in the 1985 Madrid Tennis Grand Prix event.