Please don’t add regions manually, if you enabled Regions they are managed automatically when you change location for existing listings or add new ones. Automatically added regions are searchable (e.g. if someone searches West Yorkshire), while manually added are not.
If you mean combining an attribute with region currently there’s no such option, but it’s on the roadmap. You can also search by Leeds and select the Pets filter in the search form, and then use this search URL (it will not be “pretty” though).