Gill on Gal 6:16:
and upon the Israel of God; which is a further description of the persons, for whom he prays for these blessings; and is not to be understood by way of distinction from them, but as an amplification of their character; and as pointing out the Israel, by way of emphasis, the Israel, or Israelites indeed, the spiritual Israel, as distinct from Israel according to the flesh; see 1Co 10:18. The "Israel of God", or as the Arabic version reads it, "Israel the propriety of God"; which he has a right unto, and a claim upon; who are chosen by him, Israel his elect; who are redeemed by him, out of every kindred, tongue, people, and nation; who are called by his grace, and are styled Israel his called; who are justified in his Son, and by his righteousness; and for whose sake he is exalted as a Prince and a Saviour, to give them repentance and remission of sin; and who are, or will be saved by him, with an everlasting salvation; and is a name that includes all God's elect, whether Jews or Gentiles: though it may have a particular respect to such of the Israelites, or Jews, God had foreknown and reserved for himself; and who believed in Christ, and walked as new creatures, without confidence in the flesh. The Jews themselves own, that strangers, or proselytes, shall be called by the name of Israel; so they {b} explain Isa 44:5, latter part.
Jamieson, Fausset, Brown on Gal 6:16:
16. as many--contrasting with the "as many," Galatians 6:12.
rule--literally, a straight rule, to detect crookedness; so a rule of life.
peace--from God (Ephesians 2:14-17, 6:23).
mercy--(Romans 15:9).
Israel of God[/U]--not the Israel after the flesh, among whom those teachers wish to enrol you; but the spiritual seed of Abraham by faith (Galatians 3:9,29, Romans 2:28,29, Philippians 3:3).
Matthew Henry on Gal 6:16:
The blessings which he desires for those who walk according to this rule, or which he gives them the hope and prospect of (for the words may be taken either as a prayer or a promise), are peace and mercy—peace with God and conscience, and all the comforts of this life as far as they are needful for them, and mercy, or an interest in the free love and favour of God in Christ, which are the spring and fountain of all other blessings. A foundation is laid for these in that gracious change which is wrought in them; and while they behave themselves as new creatures, and govern their lives and hopes by the rule of the gospel, they may most assuredly depend upon them. These, he declares, shall be the portion of all the Israel of God, by whom he means all sincere Christians, whether Jews or Gentiles, all who are Israelites indeed, who, though they may not be the natural, yet are become the spiritual seed of Abraham; these, being heirs of his faith, are also heirs together with him of the same promise, and consequently entitled to the peace and mercy here spoken of.