Technically, you can mix RAM as you describe. However, there is one issue that's unavoidable and one that's possible.
The unavoidable issue is that the new memory will be slower. One stick, single channel. Some motherboards will run your first 4 GB in dual-channel and only the last 8 GB in single-channel. Some will run the whole kit in single-channel. I don't know which your board will do. It's best to buy TWO 8GB sticks. Note that some boards used to be able to make dual-channel out of two 4 GB sticks on one channel and one 8 GB stick on the other, but I have no idea if this "feature" is still around.
The possible issue is that mixing modules of even the same capacity of the same make and model has been known to lead to a...