If I had the power to develop a Hitman TV show, I’d just do a straight adaptation of the games themselves. Levels could more or less be adapted into episodes, with each season representing a game.
Season 1: Codename 47 has 13 levels, perfect for a modern standard 13 episodes where each episode roughly adapts one level. The story of 47 escaping from the asylum; traveling to Hong Kong, Colombia, Budapest, Rotterdam, and back to Romania; and learning about his origins as a genetically engineered weapon. Season ends with 47 killing Ortmeyer and escaping.
Season 2: Adaptation of Silent Assassin. 47 brought out of retirement in Italy by the kidnapping of his friend and mentor Father Vittorio. Pieces together why while traveling to Russia, Japan, Malaysia, Afghanistan, and India. Discovers the kidnapping and hits he fulfilled were orchestrated by Russian mobster Sergei Zavorotko. Season ends in glorious shootout that takes out Zavorotko.
Season 3: Adaptation of Blood Money. Season begins with a hit gone wrong in Paris when 47 gets shot after taking out his targets. We spend an episode with a 47 hallucinating while on the brink of the death (a la Contracts). 47 takes out his shooters and discovers another organization is hunting him and the ICA, lead by Leland Cayne, because they want the secret of his clone technology. Season ends with a shootout in the White House and 47 faking his death to lure out Cayne.
Season 4: Adaptation of Absolution, but make it an actually good story. The pieces are all there, it just needs to be executed correctly. A rogue element gains control of the ICA (Ben Travis) who’s after Victoria, a genetically engineered person similar to 47 - but they’re opposed by Diana and 47 joins her. Things go wrong until 47 restores the order by eliminating the rogue elements of the ICA. Properly done, this could tie Season 3 and 4 together with everyone wanting their own genetically engineered assassins.
Season 5: Adaptation of the World of Assassination trilogy. Season begins with 47 going about business as usual, until discovering the Shadow Client and Providence and that they infiltrated the ICA. Maybe even callback to Season 4? Season focuses on 47 uncovering the Shadow Client, ending with meeting Grey and the big reveal back to their childhood. Season ends on cliffhanger of 47 recovering his memory.
Season 6: Continues World of Assassination trilogy story, with 47 and Grey taking down Providence.