New village screens are unlocked at the following levels: 7, 12, 16, 19, 23, 27, 32, and 36. When your village reaches these milestones, move to the lower-right corner of the right-most screen in your village and you'll be given the option to expand the village.
After ascending, a player goes back to Level 1, and normally begins again with a single screen in the new village. However, ascending lets the player carry over certain bears to the new village. If the player carries over so many bears that it would be hard to play (not enough space for new items), then the game starts the player with an additional screen so they have room to play.