An abbreviated concessive clause

Caesar was preparing to go east to do battle against the Parthians, who were creating trouble for Rome on the border if its empire, and those plotting Caesar's assassination wanted to strike before he left. Caesar had heard rumors of a plot, but he had not surrounded himself with spies, and he knew nothing of whom the plotters were or when they might strike.
["Julius Caesar" in Sulla to Julius Caesar http://www.fsmitha.com/h1/ch18.htm]

I'd like to know if "if ts empire" imply "if Parthia is Rome's empire."
Thank you in advance for your help.