does "Rayburn's aged successor"mean "the aged Rayburn?"
under the succession act of July 18, 1947, inspired by Harry Truman's affection for Sam Rayburn, the Speaker (rather than the Secretary of State, as in the past) was second in line of succession, and if both Kennedy and Johnson had been murdered, Rayburn's aged successor was now President of the United States.

Question

does "Rayburn's  aged successor"mean "the aged Rayburn?"
under the succession act of July 18, 1947, inspired by Harry Truman's affection for Sam Rayburn, the Speaker (rather than the Secretary of State, as in the past) was second in line of succession, and if both Kennedy and Johnson had been murdered, Rayburn's aged successor was now President of the United States.

Answer

No. A successor means someone who replaces someone in a job or position. So "Rayburn's aged successor" means "Rayburn's aged replacement".

Answer

"Rayburn's aged successor" means the Speaker of the House under JFK, John McCormack. Rayburn was Speaker of the House under Truman, in the 1940s, and McCormack under JFK, in the 1960's. In this sense McCormack was Rayburn's successor. Moreover, McCormack was born in 1891, so by the time he was Speaker of the House, he was well into his 70s. So Rayburn's aged successor means John McCormack, who was already very old when he was Speaker of the House under JFK.