Humble yourselves, therefore, under the mighty hand of God so that at the proper time he may exalt you, casting all your anxieties on him, because he cares for you.
1 Peter 5:6-7
Humility is a vital aspect of Christian character. Often it is in short supply in me. I confess that I am a pride-filled sinner more than I care to admit, and even not wanting to make that admission is in itself a dark manifestation of my pride. To be saved, one must humbly confess sin's control of the soul and it's impotence to make anything good. To live for Christ, that humble submission under God's rule must be sustained. Peter reminds us that God is sovereign. He will exalt us in Christ in His time.
Then this passage links a surprising problem to pride: worry. The implication is that lack of humility and surrender to God could be a common source of anxiety. And I think Peter wants us to see that. When I try to be in control, sin leads to failures, which increase my worries. I end up failing every time. So a way to defeat anxiety is to humbly submit to God's sovereign control and not fall to sin in the first place.
I see here a pattern: I must submit to the sovereign, loving rule of God in Christ with humility. When I do so, God's peace comes as I lay aside my need for control and confess that I have created my own anxieties. God will bring peace and will release me from fearful worries as I experience His care for me.