Your use case sound like a perfect fit for transfer learning.
You would have to replace your last layer(s) and retrain them or the whole model.
The strategy how “far” to retrain into the model depends on the similarity between your new and old data and the amount of new data you have.
If you have very little data, I would freeze most of the model and just retrain the final classifier. Otherwise you could be braver and retrain more. 
Have a look at the transfer learning turorial 42 for a good introduction.