The new MOT date will be the date you have the MOT done. You can NOT back date an MOT but you can have it done a little early and have the date of the MOT the same as the renewal date.
You can also drive directly to the MOT station and directly home afterwards without a current VED. You will have to have a confirmed appointment at the MOT station though, you can’t just rock up on the off chance they will carry out the test!