People still playing Battlefield 4 (and they are numerous, despite the games’ multitude of glitches) can set up both public and private servers as of today.
Rent-A-Server lets paying administrators dictate server settings and contitions i.e. server locations, map selection, mode rotations, private matches etc.
Server rentals start at only $1.49 for a single day and get cheaper from there, with a week’s rental clocking in at $6.99 and a full month (30 days) coming in at $24.99. 90 Days server rental can be purchased for $59.99. Players can rent and subsequently manage their servers via the Battlefield 4 multiplayer menu.
And remember, the quantity of servers available to rent will gradually increase over time so don’t fret if you can’t rent one initially.