See community question How do you get SourceTree to show Bitbucket team repos on New Tab > Remote? for more details.

When you try to clone a Bitbucket remote repo in New Tab > Remote, only repos from teams where you have "create repo" rights will be listed. Repos to which you have full access, but from a team where you do not have "create repo" rights, will not be listed.

You shouldn't need "create repo" rights to see/clone an existing repo. This is a pretty significant usability issue in environments with tighter access controls. And it's not consistent with how Bitbucket itself behaves. In Bitbucket you'll see all repos to which you have access, regardless of "create repo" rights.