Will a new floor solve a squeak?

Not reliably, and this catches a lot of people out. If the noise is coming from the subfloor separating from a joist, that connection is still there after new flooring goes over it, and the squeak comes back. Replacing flooring only solves the problem if the flooring layer itself was the cause, which is the less common case. It is worth diagnosing before spending on a new floor.