Here observe, that both duties are enjoined in one and the same precept, and also with one and the same penalty: Without which, that is, without following of both which without pursuing and endeavouring after both, no man shall see the Lord.
Indeed, if a person follows holiness, though he cannot obtain peace, he may see God provided he pursues peace, and the fault is none of his that he doth not find it; but if he does not pursue peace, though he pretends never so much to holiness, he cannot be happy, for a Christian must be of a peaceable as well as of a pious, conversation; peace and holiness, peacableness and purity, are here joined together, and he neither can be happy in this or the next world, that puts them asunder.
Observe farther, The manner how peace and holiness must be followed, namely, with intense endeavours: The original word imports a vehement pursuit, a metaphor taken from huntsmen, who follow the chase, and pursue their game though it flies before them; if peace be had, though it be upon hard terms, we must endeavour to secure it, for it can never be bought too dear, if it be not purchased by sin and baseness.
A frame and disposition of seeking peace with all, is eminently suited unto the doctrine and grace of the gospel. A forward spirit, ready for strife and contention, easily provoked, and retaining long a sense of injuries, is directly contrary to the spirit and temper of the gospel.
Observe likewise, How that holiness towards God must be accompanied with peaceableness towards man. It is evangelical holiness which is here required; which must be an inward holiness, an universal holiness, a sincere and real holiness, an humble and self-denying holiness, a growing and progressive holiness, and such a holiness towards God as is always accompanied with righteousness towards men.
Observe lastly, The absolute necessity of holiness in order to eternal blessedness, Without it no man shall see the Lord. The future sight of God in glory depends peremptorily on our present holiness, not as the meritorious cause of it, but as a necessary qualification and preparation for it, and as it is the indispensable condition of our obtaining of it. The soul is by holiness made meet and fit for the enjoyment of God in happiness, Colossians 1:12.
Burkitt, William. "Commentary on Hebrews 12:14". Expository Notes with Practical Observations on the New Testament. https://www.studylight.org/commentaries/wbc/hebrews-12.html. 1700-1703.