As far as I know, this is not possible. If you don't want anyone/someone specific to edit your family tree, you could copy it (export GEDCOM etc. and upload it again (though I think contact information such as E-Mail and telephone number won't be saved this way)) and then give only the people you want to edit the authentication to do so.
However, if your concern is not only someone's ability to edit your family tree but privacy as well (i. e. you don't want the person to be able to access the tree at all), you'll need to go a step further: Even if you have copied your original tree, you can't delete said original tree. On your "My Account" page, you'll be only given the option to "Remove" the tree - which basically means it is not displayed on your profile page anymore but can still be accessed by everyone with a link. To prevent someone with a link from seeing your family tree, you have to manually delete the members of said tree (which can be a huge pain if your tree is larger).
Hope this helps!
