In many cases, the ability to sense things at range or through barriers should be treated as a Create Advantage action, or as a declaration of facts by spending a Fate point. When learning a particular fact resolves a problem that the PCs are facing, ESP could also be rolled as an Overcome action.
The GM should look carefully at the role of ESP-type powers in the campaign, and make sure that such things don't short-circuit the adventure (or the fun) of the game. One common weakness is psychic stress - the character receives a Consequence or other medium-duration condition as a result of the intensity of their visions.