The Reserve Bank of India (RBI) is the central bank of India, and it is headed by a governor who is appointed by the Government of India. The governor is typically appointed for a term of three years and is eligible for re-appointment.
As of my knowledge cutoff, the longest-serving governor of the RBI was Dr. Manmohan Singh, who served two consecutive terms from September 22, 1982 to January 14, 1985, a total of two years and four months. Dr. Singh is a well-known economist and politician, who later served as the Prime Minister of India from 2004 to 2014. He is also known for his role in liberalizing India’s economy in the early 1990s as the country’s finance minister, which helped launch India on a path of rapid economic growth.
Please note that my training data is until 2021, and if any change in the governor’s tenure then it might not reflect the same in my answer.