we have update code
Topic summary
Goal: move the Dawn theme’s search icon from the top-left to between the Account and Cart icons on the top-right.
Initial guidance: one helper suggested editing header.liquid to relocate the search markup between the Account and Cart icons, noting potential UI bugs (e.g., search bar opening above the icon) after the move.
Outcome for original poster: a contributor (KetanKumar) implemented changes directly on the store; the OP confirmed the search icon was successfully repositioned, but the exact code changes were not shared publicly.
Alternative approach: another user provided a CSS-only solution using flex order in assets/base.css to reorder header__search, account, and cart icons. The OP did not test this, but it may help others.
Further assistance: for a second site, Ketan supplied a base.css snippet (under @media min-width: 990px) to toggle .header__search display based on header classes (header–top-center vs. others), along with steps to add it via Edit code.
Current status: OP’s issue is resolved. Additional users requested help and confirmation for Dawn v10.0 compatibility; those follow-up questions remain open. Code snippets (CSS/markup) are central to understanding the solutions.