Brister is a surname. Notable people with the surname include:
Bubby Brister (born 1962), former American football quarterback
Jen Brister (born 1975), stand-up comedian from South London
Mark Brister, humanitarian, baptist pastor, and former university president
Pat Brister (born 1946), business woman and Republican politician from Mandeville
Robert E. Brister, United States Navy officer during World War II
Scott Brister (born 1954), former Justice of the Supreme Court of Texas
T. C. Brister (1907-1976), former member of the Louisiana House of Representatives from Rapides Parish
Wanda Brister (born 1957), American opera tic mezzo-soprano and voice teacher