One of the most common ways to keep pants up without a belt is to wear suspenders. These straps fasten both the front and back sides of the pants, so they won't let them fall down. They are also a good option during cold weather, as they are comfortable and warm.
Safety pins can also be used to tighten up pants. These are usually small and unobtrusive, so they are a great choice for this method.
Another option to fix loose pants is to wear a pair of shorts or leggings over them. This will bulk up your waistband and make it fit better again!
Elastic can be a great solution for this as well. Just make sure that you buy the right size for your needs.
Clips are another way to keep your pants up without a belt. These come in all shapes and sizes, but you'll want to buy clips that are specifically for clothing. These are also less likely to snag your pants or cause discomfort as the metal clip catches.
Other options include a bungee cord or shoe lace that you can wrap around the pants and then tighten to your liking. This will take a little bit of time and practice to get the correct tension, but it can be a convenient and cost-effective alternative for many.
Finally, if all else fails, you can pay a tailor to alter your pants to a different fit. This can be done for a relatively minimal fee, but you will need to find a tailor who is familiar with the style of your pants.