I agree that the materials look like rhino horn but it should be confirmed in the hand.
Regarding the indicators mentioned by Gustav differentating this hilt from the modern ones, I see 4 of them:
. The shape of the worn-out nose with distinct nostrils.
. The earlobes (or earrings) have a different shape than on the modern hilts.
. The small carving above the tumpal motif on the front depicts the male organs according to Jensen.
. The carving at the base of the tumpal motif depicts the female organ according to Jensen.
Accordingly I believe that this hilt is very old.
Regards