Currently, Bitbucket Cloud offers the read, write and admin permissions to be assigned for a user.
Read is the least privileged permission, which will allow the user to view, clone, and fork the repository code but not push changes. Read access also allows users to create issues, comment on issues, and edit wiki pages.

This feature request is to add a new level of permissions that just allows a user to "View" the repository content in the UI, but that will not allow the user to clone the repo.