Rebuilding a site that already exists is a different job from starting fresh. There's usually something worth protecting - existing pages, existing search visibility - and that shapes how the work is approached.
The visible part of a redesign is the design. The part that causes problems afterwards usually isn't - it's what happens to the existing pages, their addresses, and the content search engines have already indexed.
When URLs change without anything pointing the old ones to the new, previously indexed pages stop resolving and links from other sites lead nowhere. Content that was quietly bringing in visitors sometimes gets removed during a tidy-up because nobody checked what it was doing.
Which is why a redesign is worth approaching with the existing site properly understood first. What that involves depends on how big the site is and what shape it's currently in - easier to assess by looking at it than by describing it here.
A general outline. What actually applies to your project is worked out together, before anything is agreed.
Understanding what's there now - the pages, the structure, and what's already working.
Working out which content and pages should be kept, and what genuinely needs changing.
The new design applied over a structure that keeps hold of what mattered on the old site.
Handling old addresses, checking things over before launch, and keeping an eye on it afterwards.
Send me your current URL. I'll take a look and tell you honestly what I'd be careful about - including whether a full redesign is the right move at all.