You’ll still need to move out of your old place unless you are able to negotiate a month-to-month deal with your previous landlord. Chances are they already have someone lined up for our old apartment. In that case, you will need to find a storage solution for your belongings. You can either rent a unit from storage companies or see if the movers you are using have their own storage units. If they do, they will move your belongings into and out of storage.