From Bulbapedia, the community-driven Pokémon encyclopedia.
A Pokémon Trainer's license, also known as a Pokémon handler's license or simply a Pokémon license, gives the bearer the right to own Pokémon.
In the anime, applicants must be 10 years of age or older.
In the games
According to the blurbs of Pokémon Red, Blue, and Yellow, Red (the playable character of these games) obtained his Pokémon Trainer's license and has set out to become a Pokémon Master.
In the anime
In Pokémon - I Choose You!, Ash was excited that he could get his Pokémon license now that he was ten years old. In The Battling Eevee Brothers, Rainer tells Mikey that he could lose his "Trainer qualification" for leaving his Eevee alone tied to a tree.
However, despite the case of Ash or other characters such as Bonnie, who is specifically stated to be too young to have her own Pokémon, children under the age of ten have been shown to own Pokémon. It is generally an accepted fandom theory that minors under the age of ten may own Pokémon, but are not allowed to compete in Pokémon League-sanctioned tournaments or challenge Gym Leaders.
In the manga
In The Electric Tale of Pikachu manga
According to The Electric Tale of Pikachu manga, potential Trainers are required to attend a half-day training session before qualifying to take a brief test. Those who pass the examination receive the license. Only licensed Trainers are legally allowed to purchase Poké Balls.
In other languages