What about existing private pilots flying LSA?

Pilots with an airplane private or higher pilot certificate may legally fly an LSA airplane as long as they are current to fly airplanes. However, it is advisable to get a checkout by a qualified instructor before attempting to pilot the LSA that you intend to operate. These aircraft may exhibit characteristics quite different than other aircraft that you may be familiar with. An existing pilot, private pilot for example, may fly as a sport pilot even if their medical certificate has expired, so long as they have a valid driver's license for medical eligibility.