It could be due to separation anxiety, but I suspect the dog is not barking because she is fearful and nervous. The dog will need ample time to adjust to her new surroundings and be comfortable with her new "pack", (the owners). Do you have any idea how long the elderly gentleman had her before you? Has she been shuffled from home to home? She does sound a little insecure.

How old is the German Shepherd Dog? They are my favorite breed, by the way. Every GSD I have ever had was timid during their first year or so of development. Once they matured, the dogs were bold and courageous. I would give her a lot of time and love to allow her to adjust and feel comfortable in her new surroundings. Hopefully she will start warming up to you soon. Once she feels that you are her family, she will likely start barking to alert you to whatever may be going on around her. Good luck and best wishes to you and your dog. -PetCaretaker

Thank you for the response Rhopkins. I hope your dog makes a smooth transition to her new home and will feel more at ease before too long. Congratulations. (I love GSDs). --PetCaretaker