Most pre-trained CNN models accept a $224x224$ input size when they were trained. Can I use $256x256$ to get a higher accuracy?
If you change the image size, you will be able to reuse only part of the original network.
Convolutional and pooling layers can be applied to images of any size, so the initial part of the network, which normally consists of convolutions and pooling, will be reusable as-is.
However, the dense layers after the convolutional part assume certain input dimensions. Therefore, as your larger images lead to larger input to the dense layers, you won't be able to reuse the dense layers.