It is unlikely that you can get a driver's license in Missouri while your license is currently suspended, revoked or cancelled in Kansas.
The Missouri Department of Revenue (DOR) states that for a new resident to obtain a driver's license they will need to show their out-of-State driver license (valid, or expired no more than 184 days). You must also show acceptable documents for proof of Lawful Presence, Identity, and Residency, so you cannot live in Kansas but try to obtain a driver's license in Missouri because your KS license is suspended.
When applying for a driver's license in Missouri the DOR will check the National Driver Register (NDR) and its Problem Driver Pointer System (PDPS) as is a federal requirement that all states in the US do when a person applies for or renews a driver's license.
The National Driver Register is a database whose administrator is the National Highway Transportation Safety Administration (NHTSA). This national database contains information provided by all states driver licensing officials for drivers whose licenses have been canceled, denied, revoked or suspended or who have been convicted of certain serious traffic violations.
Under Missouri law, out-of-state violations, suspensions and revocations found on the NDR can affect driving privileges in Missouri and keep a new resident from obtaining a MO driver's license.
If you went to apply for a driver's license in Missouri then a representative for the MO DOR would check the NDR and see you have a sanction on your driver's license in Kansas. The DOR should then turn you down for a license in MO until the issues in KS are dealt with and you are able to reinstate the Kansas license. Once this is done you should be able to apply and obtain a license in Missouri, though you may need to show a reinstatement (clearance) letter from Kansas to do so.
You did not say how you lost your license or for how long, so you may want to contact the Missouri DOR directly to discuss your situation and see if there is any type of license you could obtain there at this time. Keep in mind that even if you were able to get a driver's license in Missouri you still could not drive in Kansas while your driving privileges there are suspended or revoked.
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