Adding to Juan's answer:
It depends on the new operator (I intentionally didn't say owner). If the new operator is leasing the plane for a short time, they usually just use easily removable decals (which may look ugly after some flying).
Even if the operator doesn't change, the plane is repainted usually once every 5 to 8 years as this KLM blog explains. In this case the old layer is indeed removed.
Sanding and stripping
An aircraft can be disrobed of its old paint coat in a number of ways. A Fokker is sanded by hand with a sander. A Boeing or Airbus is partially sanded, partially stripped. Stripping is carried out using a liquid which, at 25°C, can strip an aircraft of all its paint in 24 hours. Once all the old paint has been removed, the primer is sprayed onto the aircraft. It takes around six hours for each layer to dry.
