Hebrews is a great text, and from cover to cover spurs the believer on in their faith. There are many warnings about faith which is not sincere. Here's your passage as sourced from biblehub.com
Holiness and Saints
Your word 'holiness' from Hebrews 12:14
ἁγιασμόν / hagiasmon is from the root
ἅγιος / hagios, which means to be set-apart/holy/different. The Temple and religious acts were considered 'hagios' because they were set apart from the normal pieces of everyday life, which is not far from the Hebrew idea of holiness either: they were special and set apart.
This is the same word which is translated all over the New Testament as 'saint': all Christians are saints, a 'set apart people', ones who are different. And that is a reality in God's sight, even when it is not a perfect reality on earth.
It's an ideal which we strive towards, but it does not contribute to our own righteousness at all:
"It is because of him that you are in Christ Jesus, who has become for us wisdom from God--that is, our righteousness" - 1 Corinthians 1:30
"...and be found in him, not having a righteousness of my own that comes from the law, but that which is through faith in Christ--the righteousness that comes from God on the basis of faith." - Philippians 3:9
And what's more, as Christians who live and walk in the guidance of the Holy Spirit, we naturally outwork that righteousness and holiness in how we live. In other words, we don't try harder to be holy, but rather we seek to walk in the guidance of the Holy Spirit.
"In him you also, when you heard the word of truth, the gospel of your salvation, and believed in him, were sealed with the promised Holy Spirit, who is the guarantee of our inheritance until we acquire possession of it, to the praise of his glory." Ephesians 1:13-14
"For the law of the Spirit of life has set you free in Christ Jesus from the law of sin and death. For God has done what the law, weakened by the flesh, could not do. By sending his own Son in the likeness of sinful flesh and for sin, he condemned sin in the flesh, in order that the righteous requirement of the law might be fulfilled in us, who walk not according to the flesh but according to the Spirit." - Romans 8:2-4
Ultimately, as Christians living under the New Covenant, our sins are covered by the blood of Jesus, which makes us 'righteous' (right-with-God). Our unrighteousness is covered by His righteousness, and the Holy Spirit enables us to walk in pure ways going forward.
One of the core messages of Hebrews is giving warning to those who call themselves Christians, but do not live out that obedience. The overall message of the book is that if our faith is genuinely set on Jesus and we walk in that proper obedience, we will see the results as we live. If we see no results at all, then we must question whether we really have that new life:
"Therefore, if anyone is in Christ, the new creation has come: The old has gone, the new is here!" - 2 Corinthians 5:17