Hi @AXVill, right now you can't rejoin a private group you left - you would need someone currently in the group to re-add you.
We're considering a feature that will allow channels to work more like the Direct Messages list, so you would be able to "close" a private group and have it show up in a "More" list and then you would be able to re-join the channel.
If you were the last person in the Private Group, there's no way to re-join right now. We will probably change the option for the last person in a Private Group to "Leave & Delete" so channels aren't left in a state with no owners.