How to add a new category to a existing trained deep learning model?
You cannot do that without re-training at least part of the model.

You will have to replace the existing output layer with a new output layer that has the desired number of neurons. That, of course, means that you will have to retrain at least the last layer or the last few layers. But you can freeze the weights of all the other layers.

In keras you can freeze the weights of a specific layer by setting its trainable property to False.