There comes a time when the old website is looking a bit old and tired and you want a nice new shiny one. Somethings to keep in mind though...
Your old website may have been around for a while and built up a bit of a following. It has also probably grown somewhat, especially if you've been running a blog or news pages.
So it's decision time, do you go with a new developer or stick with the one you know? Well that is up to you. When we are developing a new website we look at the original website and discuss what if any of the content needs to be carried forward to the new website. Sometimes there is a lot. We then look at the original CMS, Wordpress, Joomla etc and see if that can be used. Sadly, all to often the original was based on a template that makes this difficult to do properly.
So we design and build the new website. We need to remember that the links to pages in the old site may well still exist all over the internet and that the links on the new website will probably be different. Where possible we will redirect such links to the page that is the closest equivalent to the old website. Your hard worked link building won't be wasted.
Only too often have I seen this happen to new websites from supposedly respectable developers. Old links in customers bookmarks, links on other websites and listings have not been considered and the result is the infamous Error 404 where a page can't be found. I consider this to be impressively unprofessional and a really bad for your SEO or search engine optimisation as Google hates to get 404s.
So two thoughts. Firstly all the websites I design and build can be easily migrated to new designs whoever the new developer is. I always ensure proper redirects are in place so that Google never gets a 404.