Peter "Petey" Grogan was formally the Deputy Commissioner under Gillian Loeb who was appointed as acting commissioner then Commisioner of the Gotham City Police Department after Commisioners Loeb's, forced exit.
Peter Grogan, after being appointed Police Commissioner, after having been Deputy Commissioner prior and proved himself to be even more crooked than his predecessor, Gillian Loeb. A few years later, he was replaced as commissioner by James Gordon.
In other media
Batman: Arkham Origins
Peter Grogan is mentioned in the Cold, Cold, Heart DLC for Batman: Arkham Origins. He is initially planned to be the Commissioner after Gillian B. Loeb was murdered on Christmas Eve by the Joker (whilst disguised as Black Mask). However, anonymous envelopes are sent various media outlets expose him and Mayor Hamilton Hill as corrupt, including evidence strongly implicating them being on the Falcone family's payroll. This results in a lengthy protest by angry citizens that only ends when Hill resigns, destroying his chances of becoming Commissioner.