It’s a new feature that lets you team up with a friend online in Division Rivals against other solos or duos, in Squad Battles against the AI, or kick back in FUT Friendlies House Rules against other players.
In FIFA 21, there is a new friends widget, which is accessible through most of FIFA Ultimate Team by simply hitting R2 or RT. From this widget you can select a friend to play a game with and be taken straight to the Co-Op lobby.

Invite Friends
The person who sets up the lobby will become the Captain, meaning that they have control over which of their squads will be used for the match and what game mode you will play. From the lobby, both players will see the Captain’s top-rated players from their current active squad and when both players are ready the captain will have the ability to start the game in the chosen mode.
FUT CO-Op is available for both generations but you won’t be able to play across console generations or cross-play in FIFA 21. You and your friend will have to play online on the same console (for example, you cannot be on a PS4 and he on a PS5).
On the pre-match screen, you can see the connection bars of both connections (you and your friend).
Using the FIFA Trainer in a Co-Op game will show the inputs for both players on the team as they’re happening. This will allow players to see what their partner is about to do, enabling them to react to the on-screen displays. This helps in setting up the right runs without a need to rely on voice communication exclusively.
FUT 21 does not have support for game invites from Co-Op sessions, not even on FUT Friendlies. In other words, you cannot play against other friends picked by you. You will always face random opponents.
Yes. There is a toggle that lets you choose between a mix of solo players and Co-Op groups in your matches, or just vs solo players.

FIFA 21 Co-Op Options
Playing online cooperatively with a friend is only possible in Squad Battles, Division Rivals and FUT Friendlies. You cannot play FUT CO-Op on FUT Champions or FUT Draft.

FIFA 21 FUT Co-Op Modes
Excepting for FUT Friendlies Co-Op matches, there is a limit to the number of games that you can play that counted towards your weekly score: 42 for Squad Battles and 30 for FUT Rivals. When opting to play Co-Op in these game modes, both players will use one of their scored weekly matches.
In Friendlies, you can pair up to play together and, using in-game matchmaking, find people to play any of our base Friendlies experiences. The matches will follow the ruleset chosen and rewards will be the same as playing Friendlies solo. This is a great way to try out some new player combinations, teams, or to just work on your team play in a risk-free friendly environment.
Classic, Mystery Ball, Swaps, King of the hill, Max Chemistry, Headers & Volleys, Survival, Long Range and No Rules.
In Squad Battles and Rivals, based on the result of the game, each participant will earn their weekly score and coins for the match using the regular in-game calculations. With each game counting towards your number of scored matches, playing well together will be an important factor for both of your success. In Co-Op Friendlies, rewards are the same as playing Friendlies solo.
If one player has run out of games that count for their weekly score, neither of you will continue to earn weekly score. That being said, the both of you can still play the match to earn Coins & Skill Rating, make progress towards Objectives, and accumulate Weekend League Qualification Points. You will know before starting the match if this applies as both players will receive a message warning if they are out of matches.
For Division Rivals specifically, matchmaking will be done using the highest Skill Rating of the duo. So if the host is in Division 9 and the guest is in Division 5, players will be matched at the higher Skill Rating of Division 5 using our existing matchmaking for Division Rivals.

Your progression in Rivals will be similar to if you were playing games against players at your own level. So while you’ll still rise, Co-Op will not serve as a major accelerator to your ranking.
Playing together won’t only take place on the pitch in head to head gameplay. In FUT Events you can collaborate and compete by completing Objectives in-game to unlock rewards as a community. This year, two new types of Events are being included into Objectives:

Community Events
With Community Events, each player who completes Objectives in specified groups will contribute to a global XP pool. As this pool of XP grows, the community will progress towards thresholds that unlock rewards for everyone who’s completed at least one objective in the event.

Team Events
Team Events will divide the community into different teams to compete head to head for rewards. Joining a Team is easy, when you start the Event you’ll be given the choice to support one of up to five Teams each with their own set of Objectives and rewards. Competitions are balanced based on which Team’s members are contributing the highest XP on average for the event. So once you’ve chosen your Team, start completing the Objectives to help your chosen side in the leaderboards. At the end of the competition the winning Team will be rewarded with new customization Items to show off your allegiance, Coins or Packs. The types of rewards available will change with each Event throughout the year.