If your website was built a while ago then there may come a time when it needs to be updated. It may just be the design and layout that needs to be updating which may be able to be done relatively quickly. If you need to add or remove functionality from the website then this may take a little longer.
It is not good practise to make big changes to a website whilst it is live. You need to take a copy of the website and upload it on to a server so it can be worked on without affecting the rest the site.
You need to bear in mind that if something goes wrong whilst you are making changes to the site and it may mean that the you have to take your whole site offline or that parts of your site stop working without you realising.
It may be that some of the changes can be done through the CMS which you may be able to do i you have access to it. You need to be very careful when making changes through the CMS as this can sometimes cause issues and break the layout of the site.