Yes, in most cases you can keep the website you already have and add booking to it rather than starting again. There are two common ways this is done. The first is to put a search panel on your existing pages, so a visitor types in their dates on your home page and is carried through to the booking pages. The second is to run the booking portal on a web address that sits under your own domain, styled with your logo, colours and fonts so it feels like one website to the traveller.
Which of the two suits you depends mostly on how your current website was built and how much freedom you have to change it. If you or your web person can add new pages and drop in a search box, the first option usually works well. Some website builders lock down what you are allowed to add, and in that case the second option is the simpler and safer route. Neither one requires you to throw away the pages, photos and text you have already paid for.
Be aware that matching your existing design exactly is not always possible. How close it gets depends on how flexible your current theme is, and some steps such as payment and the final confirmation need to run on the booking pages so that supplier and payment rules are respected. What is included in the styling work can also vary with the plan you are on, so it is worth asking before you commit.
The useful next step is to find out who looks after your current website and whether you are able to add new pages to it, then share that with us so we can tell you which of the two approaches fits you best.