He first appeared in Complications where he was furious with Alexx for not talking to him on the case of Sara Foster, a woman who had died during surgery. He also told Alexx that he'd like to see her work on three posts a day while struggling to pay alimony to two ex-wives he'd divorced.
He later got his revenge on Alexx by talking to the boss who agreed that Alexx herself should share the burden of his work which left her completely shocked as she began working on a stabbing victim.
His final appearance was in the Season 3 episode, Addiction where yet again he clashed with Alexx on the fact that she'd hired a former alcoholic Derek Roddison to help her without consulting him on the matter.
After being exposed as the one responsible for stealing a flask from a stab victim, Glenn faced an angered Alexx who told him to go to the Chief Medical Examiner so that he could get some help but he refused.
Later on in the day, Monroe's body later wound up at the morgue after he was involved in a drunken hit and run that not only killed a young teenage girl but ended Monroe's life as well, leaving Alexx devastated by his death.