Bring carrots, orange zest, orange juice, apricots, lemon juice, 1/2 teaspoon salt, 1/4 teaspoon pepper, and cinnamon to a boil in a 12-inch nonstick skillet over medium-high heat. Reduce heat to medium-low, cover, and simmer, stirring occasionally, until carrots are nearly tender, 8 to 10 minutes.
Remove lid, increase heat to medium-high, and cook until liquid is reduced to 2 tablespoons, 1 to 2 minutes.
Add sugar and butter and cook, stirring frequently, until carrots are tender and glaze is thick and glossy, 1 to 2 minutes. Season with salt and pepper to taste. Serve.