Step 1: Recall the One Nation One Election initiative.
"One Nation One Election" aims to synchronize Lok Sabha and all State Assembly elections to be held simultaneously, reducing costs, governance disruption, and the frequency of Model Code of Conduct periods.
Step 2: Identify the High-Level Committee chairperson.
The Government of India constituted the High-Level Committee in September 2023; it is chaired by former President of India Shri Ram Nath Kovind; its members include Union Home Minister Amit Shah and others.
Step 3: Eliminate other options.
Justice Ranjan Gogoi and Justice N. V. Ramana are former Chief Justices of India; Amit Shah is a member, not the chair; Ram Nath Kovind, as former President, was chosen to head this committee, making him the correct answer.
\[ \boxed{\text{Shri Ram Nath Kovind}} \]