Chullin 130 - Foreleg, Jaws and Abomasum
The foreleg, jaws, and abomasum of a slaughtered animal are a portion of a kohen; one should separate them and give them to the kohen of his choice . This law is called "the law of gifts." It does not depend upon land, and therefore should apply inside of the Land of Israel and outside, whether the Temple is standing or not. However, in practice people follow the more lenient opinion of Rabbi Ilai.
The law of the gifts applies to regular animals but not to consecrated ones. Actually, one could decide that it does apply to the consecrated animals, with the following "a fortiori" argument: since unconsecrated animals, which are not subject to the law of breast and thigh - which must be, in the case of peace offering, given to the kohen and his family to eat - are nevertheless subject to the law of gifts, then consecrated animal, which are subject to the law of breast and thigh, must surely be subject to the law of gifts! To dispel this notion, the Torah said, " I have given them (breast and thighs) as gifts " - meaning, only "them" but not the foreleg, jaw, and abomasum.
Art: Pieter de Grebber - Elisha Refusing Gifts From Naaman