Final answer:
Carter Glass was the opponent of the Martin Organization and filled Senator Martin's vacant Senate seat after his death.
Step-by-step explanation:
The prominent opponent of the Martin Organization who was appointed to fill Senator Martin's vacant seat following his death was D. Carter Glass. Carter Glass, who was a newspaper publisher and Democratic politician from Lynchburg, Virginia, played a significant role in the realm of American politics over a span of several decades.
He opposed the Martin Organization, a powerful political machine in Virginia, for over 20 years before eventually becoming Martin's successor in the U.S. Senate after Martin's death in 1919.