The cavalier is a fairy chess piece that improves on the gryphon by correcting the gryphon's asymmetric retreat: the gryphon cannot exit the way it arrived.
(Is the cavalier actually an improvement? Or does this peculiar feature of the gryphon make the game more interesting?)
The cavalier's move can be either a ferz move followed by an outward rook move or a rook move followed by an outward ferz. The two possible paths prevent the asymmetric blocking possible with the gryphon.
The cavalier's range is slightly different from the gryphon because in its rook move, it must step at least one square. However, a cavalier ferz compound does have the same range as a gryphon.
In terms of range, cavalier = gryphon - ferz. We can also consider similar subtractions to sliding pieces: a rook minus wazir, bishop minus ferz, queen minus either or them, or queen minus king. The intervening (subtracted) square must be empty. If we want jumping, we can add that back in with alfil or dabbaba. Jump and slide on the same move remains impossible though. If it were possible, we'd have asymmetric retreat problems again.
These "minus sliders" are nice components to make compound pieces out of. The abilities are disjoint.
A piece that makes one ferz then one wazir move, in either order, both outward, has the same range as a knight but requires at least one of the intervening squares to be empty.