Albert Barnes Commentary 1 Samuel 9:24

"And the cook took up the thigh, and that which was upon it, and set it before Saul. And [Samuel] said, Behold, that which hath been reserved! set it before thee and eat; because unto the appointed time hath it been kept for thee, for I said, I have invited the people. So Saul did eat with Samuel that day." — 1 Samuel 9:24 (ASV)

The shoulder and its accompanying parts accurately conveys the meaning. The right shoulder was the priest’s portion in the Levitical sacrifices. Probably it was Samuel’s own portion in this case, and he gave it to Saul as a mark of the highest honor.