If you want to play on the newly-available maps in Evolve, you'll need to log in to the game's multiplayer mode and the content should automatically download via the latest micropatch.
The maps will not download if you're playing in Solo Mode.
However: If you are playing on either an Xbox One or a PlayStation 4, you will need to have active subscriptions to either Xbox Live Gold or PlayStation Plus to access this content (as these services are required to play Evolve's online modes).