Does it exist a script to teleport from a public game to a private game?

"Does it exist a script to teleport from a public game (of mine) to a private game (still of mine)

It depends on who you are teleporting.

If it is private, then only you can join while the rest of the players cannot.

Perhaps you could make the game only accessible through a reserved server.

It's possible to make it so that if the game is ran on a reserved server, players can be teleported into it and if the game is played directly, not teleportation, the server can shutdown.

You can learn more about TeleportService here: https://developer.roblox.com/en-us/api-reference/class/TeleportService