Anne Leek was educated at Juilliard where she received her bachelor of music, master of music and doctor of musical arts degrees. During her time in New York, she performed on a recital in Carnegie Hall sponsored by the Artists International Contest, which she won. During the 1980s, Leek was Solo Principal Oboe of the Mannheim Orchestra in Germany.
Before joining the Houston Symphony, she played a two year position as principal oboe in the Pittsburgh Symphony, under the baton of Lorin Maazel. Along with her career as an orchestral musician, Leek has taught at Indiana University, Arizona State University and has taught at the University of Houston. As a recital soloist and chamber musician, she has appeared in numerous major cities across the world.