Besides that that his hand shall get, i.e. besides what he shall voluntarily promise and give according to his ability.
Related Commentaries of Numbers 6:21
Numbers 6:21
21 This is the law of the Nazarite who hath vowed, and of his offering unto the LORD for his separation, beside that that his hand shall get: according to the vow which he vowed, so he must do after the law of his separation.