High resolution GAN

How can I work with high resolution images (256px) with a GAN model that works only on low images (64px)?
Can I add some layers or anything else to support that?

Technically your model might already be able to accept larger input shapes. However, using high-res inputs might be tricky as the model often failed in the past. You could take a look at e.g. the StyleGAN paper and check its training schedule (also check newer papers, as the scheduling might have been improved already).