Calendars being what they are, comparing the past and present datings, it would be a stretch to say that Bible characters made New Years resolutions. Rosh Hashanah, the Jewish New Year would have been celebrated September 4-6 on the modern calendar. So, with calendar adjustments from culture to culture it's hard to say when the New Year would have been celebrated in Bible times.
Still, when I search "resolved" in my HCSB Study Bible on line app, there are a couple of interesting hits. For example, when Jehoshaphat and the armies of Israel faced the Moabites, Ammonites, and Meunites, the Chronicler wrote, "Jehoshaphat was afraid, and he resolved to seek the Lord" (2 Chronicles 20:3). Then, in his longest Psalm, King David wrote, "I am resolved to obey your statutes to the very end" (Psalm 119:112). Interestingly, Solomon wrote, "I have tested all this by wisdom. I resolved, 'I will be wise', but it was beyond me" (Ecclesiastes 7:23). In the Prophets there are a couple of references, mostly about what God's resolved to do in the nation. in Acts, Paul resolved to pass through Macedonia and Achaia on his way to Jerusalem.
Several of these "resolved" passages are interesting. For instance, David's resolution to obey God's commands to the very end. Of course, the context of that verse is His love and dependence on the Word of God. Earlier he had confessed that God's Word was a lamp to his feet and a light to his path. The greater resolve is a prayer to be taught by God and find deliverance in His Word. The promise of obedience is grounded in His submission to the Father's instruction and guidance. So, his resolution to obey was contingent on God's provision of sustaining power through the Word. See 119:116.
Solomon's resolution is profound. He had resolved to be wise. Well, that certainly did define his pursuits in the life, the prayer for wisdom when he became king, and the many mentions of wisdom in the Proverbs and Ecclesiastes. His resolve, however, was bigger that humanly possible. You see, Solomon knew wisdom comes from the Lord, and that it derives from fearing and reverencing God. He had written about it many times. The long of it is that his resolution to be wise was something that only God could do. It was a learning experience for him.
Here's the deal, as I see it. It's a good thing to review life, make note of strong points, perhaps lament some of the weak ones. Without some resolve we'd just keep making the same mistakes over and over again. But, even with our best intentions, our resolve must be realistic. More and more I love what John the Baptist said: "He must increase but I must decrease" (john 3:30). That puts my new directions and goals in a proper context of life, submitting everything to Him and basing all of my achievements on my growing relationship with Him.
Lose weight. I hope so. Get more exercise. Sure. Be nicer. Yes. Serve more. Naturally. They are all possible if they are secondary to Him being first in my life.
Happy New year.