Final answer:
Sydney Carton makes a deal with John Barsad (Solomon Pross) to gain access to Charles Darnay in prison by blackmailing Barsad with the threat of revealing his double espionage, which is a pivotal part of Carton's plan and the storyline of 'A Tale of Two Cities'.
Step-by-step explanation:
The deal that Sydney Carton makes with John Barsad, also known as Solomon Pross, occurs in Charles Dickens's novel A Tale of Two Cities. Carton blackmails Barsad into helping him because Barsad does not want his secret -- that he is a spy for the English and the French -- to be revealed.
Carton's leverage leads Barsad to agree to grant him access to Charles Darnay in prison, which is a crucial part of Carton's plan. Darnay has been imprisoned in the Bastille and is facing execution during the French Revolution. This deal is central to the unfolding drama and sets up Carton's ultimate sacrifice.