The shoulder and its appurtenances - would give the sense accurately. 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.
Related Commentaries of 1 Samuel 9:24
1 Samuel 9:24
24 And the cook took up the shoulder, and that which was upon it, and set it before Saul. And Samuel said, Behold that which is left! set it before thee, and eat: for unto this time hath it been kept for thee since I said, I have invited the people. So Saul did eat with Samuel that day.