The character first appeared briefly at the end of the season's second episode, standing by while Barry talked to the imprisoned Kilg%re. Brooks is set to reprise his role for multiple episodes later this season. I don’t believe anyone has reported on this, and we haven’t acknowledged that he’ll be showing up again in multiple episodes.
In the series, Warden Wolfe is the hard-nosed guardian of Iron Heights Prison, Warden Wolf relishes using the physical and psychological means at his disposal to control his prisoners… especially the super-powered inmates held in the facility’s Meta-Human Wing.
In the comics, Wolfe hates the inmates passionately, and is dedicated to ensuring they do not escape - not just for the safety of the general public, but to make the lives of his prisoners, particularly the 'Rogues' who have faced the various heroes called the Flash over the years, utterly miserable. He is keen to ensure that prisoners with particularly powerful metahuman abilities are kept in such a way that they cannot escape, and he simply does not care if this also causes them physical or psychological pain. His attitude has earned him a degree of contempt from police and the Flash, but they accept his authority due to the necessity of keeping the Rogues contained.
The character first appeared in 2001's The Flash: Iron Heights by Geoff Johns and Ethan Van Sciver, the creative team who would later go on to redefine the character in The Flash: Rebirth.
The Flash airs on Tuesday nights at 8 p.m. ET/PT on The CW.