All CO hunters, both resident and non-resident, are required to buy a small game license for $84 before they can get their name into the draw for tags for each game management unit for big game (elk, deer, moose, pronghorn, sheep, goats, bear, lion, etc). You can submit as many requests for different GMUs, for each type of season and big game (archery, black powder, gun) and I believe each submittal is a $9 fee. If you are successful in the draw you will be charged a non-resident license fee soon after your name is drawn, so you have to make sure to have a credit card on file with the CPW. The non-resident fee for elk for 2021 is s $670.25 for Bull Elk (Antlered) or Either Sex Elk tags and $503.12 for cow/calf (Antlerless).
That being said, you can also submit your name for just the preference points for all the big game species you may want to hunt at some point in future years, for $9 for each species, but you still have to buy the non-resident small game license for $84. They know up front you're not going to buy a non-resident license, and send you a confirmation each year that you gained a preference point for the species applied for. You can use these preference points to get a higher percentage success ratio of being drawn for the better and more highly sought after GMUs, those that have a higher kill ratio of the species you're after. Hope this helps.