Matthew Poole and continuators on Numbers 6:19

19 And the priest shall take the sodden shoulder of the ram, and one unleavened cake out of the basket, and one unleavened wafer, and shall put them upon the hands of the Nazarite , after the hair of his separation is shaven.

The left shoulder, as it appears from ver. 20. where this is joyned with the heave-shoulder, which was the right-shoulder, and which was the Priests due in all sacrifices, Lev. 7. 32. and in this also. But here the other shoulder was added to it, as a special token of thankfulness from the Nazarites for Gods singular favours vouchsafed unto them.

That he may give them to the Priest, as his peculiar gift.