A medical assembly implanting a transcatheter heart valve in the heart at a valve deployment site and related methods of implantation and delivery. An anchor is endovascularly introduced into the heart and implanted to a cardiac wall with an anchor delivery system and delivery cable. A second delivery system introduces a tether which coupled to the implanted anchor and a transcatheter heart valve. The transcatheter heart valve includes either a top or bottom brim which is positioned to conform to the atrial floor at the deployment site.