Let me cross some "T's" and dot some "i's".
1st of all, if you have never hunted "the west" for elk or anything else, I do not recommend a DIY hunt. Altitude, unfamiliarity of area, dramatic weather changes, vast expanse of hunting ground, long range shooting
. . . each and all can make for a miserable, unsuccessful,and expensive hunting experience. Get someone to go with you who has done it before. Or, hire a "DIY" outfitter, or . . . get with somebody at the hunt area to help you. Don't end up another stat.
2nd . . . Wyoming has a "Leftover License Draw"from July 10-20th. These are elk (deer, antelope) licenses that were NOT drawn in the first draw(s). You can see the list on-line and make application after July 10th because that is the date the resident draws are announced. They are a bit pricey: $481.00, but you would know if you drew (guaranteed a license) around July 31st (tentative drawing date). Capice?!
The Wyoming G&F link to that page is:
http://gf.state.wy.us/wildlife/hunting/formsapps/BGNonresident/index.asp
I'm in S.E. Wyoming and am very familiar with hunting in this corner of the state if I can be of any assistance.