Simultaneously working part-time and retiring part-time is compatible.
Partial retirement after retirement age occurs when you reach retirement age but decide to work fewer hours. It is a way of partially leaving work and gradually entering retirement.
Until now it was possible to reduce the working day by 50%, and from now on it will be possible to reduce it by between 25% and 75%.
In this case the proportional part of the salary and pension is paid, and the company does not have to formalise a relief contract (contrato de relevo) (check this link to find out how to anticipate the retirement through the relief contract).
Link to the General Treasury of Social Security for more information.