The Contact Public Event has been added to Destiny 2 with the Season of Arrivals. The new event can currently be found on Io, although we have reason to suspect that it might show up on Titan in the future. You can see the location of the event marked on the map below, all you need to do is spawn in at Lost Oasis on Io, and it is right in front of you.
This event plays a lot like Gambit, although it gets far more hectic towards the end. It starts at a Power level of 990, so expect to get punched around a little if you are below that. The good news is that the event is very busy right now, with lots of players, so there will be lots of people to help.
By the time it reaches the last round, the Power level is up to 1040, so be prepared to really fight for your life if you are under 990 going in.
The even is based on the rough version of Gambit. Enemies will spawn in, and you will need to kill them and collect the Dark Motes that they drop, then put these in the bank in the middle of the arena. Holding more motes will result in a higher percentage each time you deposit them. This adds some risk as if you die, you will lose the motes, so make sure you deposit them at a comfortable rate.
You need to fill the bank, and get it to 100 percent, four times throughout the event. While you are trying to do this, a timer is counting down, so you need to be fast. Blockers will spawn in from time to time, and you will need to take them out to get access to the bank again.
You should also keep an eye out for lines of energy that go from the large structure above the bank to a random area near the event. These will lead you to a platform with a Barrier, Unstoppable, or Overload Champions, and you will need to take them out to get to the Bloom, the sphere floating in the center of the platform. They can grab it and run with it, so you need to ensure you kill them as quickly as you can.
When they are dead, take the Bloom to the bank for a ten percent jump in progress. You also need to watch out for enemies getting too close to the bank, or they steal Blooms and set your progress back ten percent.
When you get to the last part, you need to fill it to 100 percent, and then take out the random Blights that will spawn in. When you kill all the Blights, the final boss will spawn, and you need to take them out before the timer runs down. You need to be aware that more blights can spawn, granting the boss immunity to damage, and you will need to take them out again to damage him.
The event ends when you kill the boss or fail by letting the timer run down while he is still alive. To make the event Heroic, you will need to bank all the Blooms that appear during the event, so prioritise those, and defending the bank, if Heroic mode is what interests you.