In the games
In Pokémon HeartGold and SoulSilver, Petrel is apparently Team Rocket's master of disguise. He is first seen dressing as Giovanni and then battled in the Team Rocket HQ. In Goldenrod Radio Tower he appears again, using his disguise skills again, this time dressed as Radio Tower Director.
Petrel's motives on Team Rocket are more mild-mannered, as he freely gives out information such as passwords and the location of the Director. He even considers himself a "nice guy" and hands over the key. In fact, it is his giving out of this information that leads to many of Team Rocket's defeats, despite his opinion that the player can't use the information anyways.
Petrel's position has existed since Pokémon Gold and Silver. However, his existence was easy to miss because all Rocket Executives used the same sprite (now adopted as Archer's canonical design), making it seem to some like there was only one Executive. The Rocket Executive that Petrel is based on was then given a canonical design and an official name in HeartGold and SoulSilver, along with the other three Executives, to distinguish them as individuals. Proton's case is the same.
In the Pokémon Adventures manga
Petrel appears in the HeartGold & SoulSilver chapter alongside the other three Executives. He, along with his fellow teammates, take control of Team Rocket from Carr, saying that they will stay true to Giovanni's intentions. In this series, Petrel is a master of disguise, and has the ability to quickly disguise himself as any person he has met.
Petrel uses his Koffing to attack Silver and Clair at the Dragon's Den but loses and has his plate stolen. Later, he attacks Silver and Eusine at the Johto Safari Zone to recover the plate he lost. Using his Pokémon, Petrel gains an advantage over the two and nearly sends them off a bridge. However, Silver manages to rise up from the water, defeat Petrel, and take the two plates he had with him. Using his disguise skills, Petrel manages to escape from Silver's grasp and escape.
Later, he joins his fellow teammates to finish their plan to capture the legendary Pokémon Arceus. They arrive at the Ruins of Alph and witness Gold battling Arceus. After Arceus sends them all to the Sinjoh Ruins, the Four Generals restrain Arceus and force it onto the Mystri Stage.
Using its great powers, they force Arceus to create the legendary Pokémon Dialga, Palkia, and Giratina. While Archer, Ariana, and Proton start tearing up at the thought of pleasing Giovanni, Petrel reveals to Silver that he knows that he is the son of their boss. He reveals to Silver that he intends to betray his teammates by lying to Giovanni by telling him that Archer, Proton, and Ariana attacked Silver. With this information, Giovanni would destroy the three while Petrel would become Team Rocket's second-in-command for acting like he was protecting Silver.
Despite being blinded by Petrel's Golbat, Silver manages to escape his grasp and fly to where Dialga, Palkia, and Giratina and still being created. Using himself as a distraction, Silver manages to stall the Four Generals long enough for Gold and Crystal to destroy the Pokémon Arceus was forced to create. Now freed from their control, Arceus uses its powers to send Petrel and his teammates flying.
As Archer begins to lose his mind, Petrel becomes scared and decides to escape. Knowing that his teammates would stop him if he appeared as himself, Petrel decides to disguise himself as Giovanni so that he can walk freely. Before his plan can be executed, the real Giovanni arrives and stops him.
After the battle with Arceus had ended, Petrel attempted to escape once more by disguising himself as Bugsy. Gold quickly notices him, and Lance captures Petrel by having his Dragonite lift him up in the air. When Gold asks how a coward like Petrel could defeat him, Lance reveals that it was because Petrel disguised himself as Yellow, a Trainer with the same powers and birthplace as him.