Hi @Tommy_V - thank you for reaching out. Private boards are currently available on Starter, Education, Business, and Enterprise plans. 

If you're the Admin, you can configure default sharing settings for newly created boards. 

1. Go to Team settings > Permissions > Sharing settings. 
2. Choose Only board owner can access under Default settings for board sharing. You can also configure Project sharing settings there.

Also, make sure the board will not be created in a shared project. If the board is located in a project, it automatically gets shared with all project members. Thus, before creating a board, switch to Boards in this team tab to ensure that the board will not get into a specific project.

You can learn more here. I hope this helps!

@Tommy_V 

If I make a board and don't share it, can the Admin still view it? Is there a way to create a completely private board?

No, and yes. While you are a member of the team, not even the Team Admin will not be able to view the board.

However, if they decided to remove you from the team, they can assume ownership of all of your content, e.g., boards/projects/custom templates – they could also choose to make another team member the owner of your content.

Regarding creating additional teams: Currently, I'm only on the education plan and can't create a free team. To set up another team beyond the educational one, I'd need to subscribe to a paid plan.

Correct. However, if you happened to have another Free Plan team associated with another email address, you could add your current email address that you use with your Education Plan team account as a member of your other Free Plan team. Once you do this, you will see two team spaces in your Education Plan account dashboard. You could even grant your Education Plan account Team Admin rights to that other Free Plan space, and then delete the other team admin, with the end result being that you now have a Free Plan space associated with your Education Plan email address/account.