Typically, something like this:
- Row 1 (bar above the header): Free Shipping, or offer
- Row 2: Burger menu icon (left), logo (middle), cart icon (right).
- Row 3: Search box
Amazon’s header on mobile is great inspiration:
- row 1: burger menu, logo, account, cart
- row 2: search box
- row 3: (scrollable) link bar
The only problem I see is that it is neither sticky nor semi-sticky (reappearing when scrolling back up).
What I’d recommend is keeping at least row 1 sticky, and row 2 (and optionally row 3) semi-sticky.
Another interesting option suggested by one of the members of my Ecom Convert group is to make row 2 (search bar) sticky and when scrolling down the burger menu drops to row 2. So effectively when scrolling down you only have what is needed: the burger menu and the search.