Varkon is a bumbling Galra rent-a-cop in charge of security in a space mall.
He is a big fan of Zarkon (evident by the poster of his emperor he keeps in his locker and how obviously similar his name is to Zarkon's) and has a sense of duty and self-importance as bloated as his belly.
He makes his only appearance in Season 2 episode "Space Mall" where, while enjoying a meal in his office, he notices the Paladins (Lance, Pidge, Hunk, and Keith) on his surveillance cameras, discarding some silly disguises, and immediately suspects them to be space pirates, disguising themselves as harmless shoppers.
He readies himself while swearing to a poster of his emperor, Zarkon, that he will protect the mall while striking a bold pose (with his gut hanging out).
He later gets a security alert from the "Slice Capades" store, and sees Keith running from the store owner (after the sleaze tried to take his knife). Varkon mounts his hoverbike and begins pursuing the supposed "space pirates".
While patrolling his mall for the "pirates", Varkon comes across a crowd of shoppers lining up in front of a fastfood joint "Vrepit Sal's" and investigates to find Hunk serving food. Upon confronting him Hunk flees and Varkon pursues.
Momentarily losing Hunk, he soon sees him with Keith just outside some restrooms and continues his pursuit. Before long, he's chasing all four of them, as they continue to flee while riding on a cow (that was free along with a purchase made by Pidge and Lance) and then Coran (who managed to buy the Scaultrite lenses they came for).
To his irritation, Varkon breaks his pursuit when the Paladins and Coran exit the mall (which is technically outside his jurisdiction) but he warns them to never come back. Seeing as he's stopped chasing them, Lance starts mocking Varkon only to get smacked in the face by a low-hanging light, which the security officer takes as a victory "That's one for Varkon!"