O romance que você está procurando é provavelmente To Live Forever de Jack Vance, publicado pela primeira vez em 1956. Ele tem o título alternativo Clarges . Acabo de começar a ler este livro, um dos poucos de Jack Vance que ainda não li, por isso não posso dizer se a cena no recinto da feira ou o final são como você descreve. Mas muito do que você lembra parece consistente com este livro.
Esta revisão da Goodreads por Kat Hooper menciona algumas das coisas que você lembra, como a competição em renome para o qual o prêmio é mais vida, os níveis ascendentes e o uso de clones.
In Clarges, a city in the far future, humans have conquered death. Unfortunately, there's just not enough room for billions of immortal people to live forever, so they've passed the fair-play act which divides society into 5 phyle which must be maintained at certain population ratios. Those who choose to participate in fair-play must register in Brood, the lowest phyle, and receive 82 years of life, after which an "assassin" visits and takes them away in a black hearse. By significantly contributing to society, citizens may move up through the phyle, adding several years of life with each step. A very select few will reach Amaranth and may have their bodies genetically modified (with 5 copies made, in case of accidents), making them youthful forever.
O link da Wikipédia para Live Forever descreve como o protagonista já havia foi um imortal e estava tentando se tornar um novamente:
The ultimate prize is the top category, called Amaranth, which offers true immortality to the fortunate few. People who achieve this distinction are accorded the honorific "The" in front of their name.
The Grayven Warlock was one of those few, but he has become a fugitive after a feud with another Amaranth resulted in the latter's death. Masquerading as his own "relict" (clone) using the name Gavin Waylock, he lives in obscurity, looking for the accomplishment that will reinstate him among the immortals. However, Waylock's dramatic stratagems result in changes to society far beyond anything he had intended.