Find a village and check farm plots or chests
Kill zombies, husks, or zombie villagers for a chance to get a carrot
Fish for a small chance to catch a carrot
Search shipwreck supply chests
Search buried treasure chests
Search dungeon chests
Search mineshaft chests
Search woodland mansion chests
Trade with a farmer villager
Use a carrot on a stick to move pigs after obtaining a carrot from any source