Will a redesign cost us our place on Google?
It doesn't have to. What usually costs a site its ranking is not the new site but old addresses that disappear without leading anywhere.

Google knows a page by its address. If a page that has sat at “yourcompany.com/our-services” for years becomes “yourcompany.com/services” on the new site, in Google's eyes the old page has vanished and a brand-new one has appeared. The trust the old page built up, the links it earned and its place in search results are suddenly left hanging.
Point old addresses to the new ones
The fix is a permanent redirect (301). Anyone who opens the old address, Google included, is taken to the new one automatically, and Google understands it as “the page has moved”. To do this, every address on the old site is listed before the redesign and each one is matched with its counterpart on the new site. Pages with no counterpart are pointed to the closest content.
The easiest way to build this list is from the old site's sitemap and the pages report in Search Console. The pages with the most visits and the most links from other sites go at the top.
Move content, don't delete it
The text, title and images of a page that ranks well are the reason it ranks. Changing the design in a redesign is fine, but if you remove the question the page answers, the ranking goes with it. Content that works should be moved into the new design and updated if needed.
What to do after launch day
Submit the new sitemap to Search Console.
Open the most important old addresses one by one and check that they lead to the new page.
Press “Request indexing” in Search Console for your important pages. Do it for the old addresses too; Google will see the redirect sooner.
Watch for “Not found (404)” errors in Search Console's “Pages” report for a few weeks, and close each address that turns up with a redirect.
Update the links on your Google Business Profile and social media accounts to the new addresses.
Short-term ups and downs are normal
Even when the redirects are set up correctly, it takes Google from a few days to a few weeks to read the new site from end to end. Seeing some positions shift in that time is normal, and the old sitelinks in search results are gradually replaced by new ones. With the redirects in place, rankings recover.
At Methodda, matching old addresses to new ones is part of every redesign we do. When we redesigned our own site, we made the same list and pointed every one of our old addresses to its new one.