Charles Ellicott Commentary Numbers 6:21

"This is the law of the Nazirite who voweth, [and of] his oblation unto Jehovah for his separation, besides that which he is able to get: according to his vow which he voweth, so he must do after the law of his separation." — Numbers 6:21 (ASV)

Beside that that his hand shall get. —i.e., besides any voluntary offerings which he may have the power to make.