Creating a new world and making it an Old World limits that specific world size to 256x256. Going into settings>video and activating "Limit World Size" will make all newly created worlds as Old Worlds. This is not what the OP is asking for.
"In the Xbox 360 Edition, PlayStation 3 Edition, PlayStation Vita Edition, and Wii U Edition, the Overworld is limited to 864×864 blocks. Additionally, in the Xbox One Edition, PlayStation 4 Edition and Nintendo Switch Edition, the player is able to further select the size of their worlds, from Small (1024×1024), Medium (3072×3072), and Large (5120×5120, Switch excluded). The edges of these worlds are surrounded by an endless sea of water, preceded by an invisible barrier." -- Source
There was mention of adding the Small, Medium, Large sizes to MCPE by Tommaso. It just hasn't been implemented yet.