Once you receive your new passport, your old passport is not valid for international travel. However, if your old passport is linked to a valid visa, you can still use the valid visa.
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Many European countries (the Schengen states) require that your passport be valid for at least three months beyond your planned date of departure from the Schengen area.
You must apply in person if your previous passport expired more than 5 years ago, was issued before you were 16 years old, or was lost, stolen or damaged.
Use your old passport and you will be able to travel anywhere as long as there is 6 months validity remaining. Might be different for each country. In the US they take your old passport while processing the new one.