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Thank you for using JustAnswer!It will be possible for you to move to a different state. What you have to do, in advance, is to have your court in MO transfer your probation to a court in TN.
In other words, your probation will not end. Rather, your probation will follow you and simply be monitored by a nearby court.
You can learn more about the Interstate Compact for Adult Supervision at: http://www.interstatecompact.org/About/NavigatingtheCompact/InterstateCompactMyths.aspx
Good luck and best wishes. I hope that you find this information to be helpful and this answer to be ACCEPTable!