A voter must vote at the poll to which he has been assigned. If a voter has moved within Jefferson County, he may change his address at any time, including the day of the election. However, if a voter has moved within Jefferson County and has not updated his voting information before the day of the election, then the voter may be instructed to travel to the new poll location in order to cast a ballot. Missouri law requires a voter to vote at a poll based on their current address, not the old address.
If you are new to Jefferson County, Missouri, you must have registered to vote in Jefferson County before the 4th Wednesday before the election. If you have failed to do so you may or may not be entitled to a provisional ballot. (If a voter moves from one Missouri county to another Missouri county they MUST re-register to vote in the new county.)