I want to release a game, then work a new version of the game separately without sharing it but still maintaining the original game as public. Then I want to release the new game under the same URL as the first one and completely replace the original game.
How would I do this?

Well, for the first part just release it as a new project, but I don't think there's any way you can replace an existing project besides just copying in all of the sprites and scripts and stuff. Or, you could try playing with the “Import project” feature after deleting all existing sprites. Or, the easiest option is just include a link to the new project on the old one.

If I import the new project into the old game, will it overwrite that game?

Zygorithm wrote:

If I import the new project into the old game, will it overwrite that game?

I think you have to delete all of the old sprites and stuff first.