That Limited-Time Mode is called Power Grab, and will join the likes of Resurgence and Mini-Royale in the rotation of complimentary modes to the standard battle royale experience.
Power Grab Explained
As the official Season 3 Reloaded reveal blog states, Power Grab is "a Limited-Time Mode that pits over 100 Operators across select squad sizes in a battle for true badass protagonist supremacy."
What you need to do is survive storm zones, as you do in any Warzone match, with there being no Gulag this time. Instead, you can either buy teammates back or revive them by collecting Dog Tags.
This works somewhat like Kill Confirmed does in standard multiplayer modes. Upon death, players drop dog tags for other players to collect.
As you collect them, you'll climb a ladder of rewards. Those rewards include "a UAV; a Respawn Token, which gives you the right to infil into Verdansk again; and Advanced Gas Masks and Specialist Bonuses, at higher tiers." You can see the tiers of rewards on the right of the screenshot below:
That means, as you kill more players and collect more dog tags, your team will get more powerful, promoting positive play.
Aside from that, it works just as any other mode, with being the last team standing being what gets you the win.
Power Grab will join the other main Warzone modes once Season 3 Reloaded begins at 12am ET/5am BST on May 20.
It should be on the list of modes from the lobby menu, just as all modes normally are.
You'll be able to jump in and it won't affect your battle royale specific stats. It's not clear yet how many players will be in each team.