You can move and edit the columns of your public board at any time, but if you’re not the owner of the public board, you won’t be able to edit or add columns.
If you’re the creator of a team board, you can edit and add columns at any time.
In case you have a team and you want to give permission to your team member to edit and add columns, you can assign this person as an Admin of your team. After that, they'll be able to edit and add columns on your team board.
Click here to check how to assign admins to your team.