Before going into coaching, Gilstrap was an athlete at Texas, lettering in football (1921-23), basketball (1922) and track and field (1922-23).

In 1925 he became the Athletic Director at Schreiner Institute in Kerrville, Texas, which was then an-all boys military junior college.

[5] In 1937, Gilstrap returned to Texas to serve as an assistant coach on the Longhorns football team.

He led the team to the Southwest Conference Championship and the NCAA Tournament in his first year, taking them to their first Final Four appearance.

He was inducted into the University of Texas Athletics Hall of Honor in 1968 for his contributions as a player and a coach.