John Gill Commentary Leviticus 9:21

"and the breasts and the right thigh Aaron waved for a wave-offering before Jehovah; as Moses commanded." — Leviticus 9:21 (ASV)

And the breasts and the right shoulder
The breasts of the bullock and the ram, and the right shoulders of them both:

Aaron waved for a wave offering before the Lord ;
which was given to him as his part of the peace offerings, after they had been thus waved before the Lord; whereby an acknowledgment was made that he was Lord of all, and had a right to all they had; in token of which these parts were given to his priests towards their maintenance:

as Moses commanded ;
see (Exodus 29:27Exodus 29:28) (Leviticus 7:34–36) .