Blizzard has announced that the Overwatch closed beta will resume on February 9. The second round of beta testing will feature an all-new progression system, a pair of new maps, a new game mode, and a number of Private Game updates including full AI matches.
Players who were already part of the Overwatch beta last year will still have access when the game comes back online next week. We don't yet know what form the progression system will take, but you can see Game Director Jeff Kaplan discussing some previous iterations here. Blizzard said that more details about the new beta, including proper patch notes, will be released before it begins.
If you haven't yet signed up for the beta, you may do so at Battle.net.