I currently reside in KS and will be moving to MO. Can I obtain a Missouri License before my KS license is suspended in August?

You might be able to get the license in MO, but the subsequent license suspension you're expecting from KS may follow you to MO and cause the new license to also be suspended. Then you'll have to deal with two suspensions instead of only one. Consult with an experienced DWI attorney in Missouri to find out how the MO DMV will react.

I agree you may be looking at license suspension/revocation in two states if you try to get a MO license before your KS hearing. You should discuss this with both a KS and MO attorney. Good luck.