You could use transfer learning (i.e. use a pre-trained model, then change its last layer to accommodate the new classes, and re-train this slightly modified model, maybe with a lower learning rate) to achieve that, but transfer learning does not necessarily attempt to retain any of the previously acquired information (especially if you don't use very small learning rates, you keep on training and you do not freeze the weights of the convolutional layers), but only to speed up training or when your new dataset is not big enough, by starting from a model that has already learned general features that are supposedly similar to the features needed for your specific task. There is also the related domain adaptation problem.
There are more suitable approaches to perform incremental class learning (which is what you are asking for!), which directly address the catastrophic forgetting problem. For instance, you can take a look at this paper Class-incremental Learning via Deep Model Consolidation, which proposes the Deep Model Consolidation (DMC) approach. There are other continual/incremental learning approaches, many of them are described here or in more detail here.