Yes, in most cases you can bring your old customer and booking records across, so you do not have to start again from nothing.
The usual way is to export what you already hold into a spreadsheet, one row per customer or per booking, and then have that file loaded into the new system for you. Names, contact details, addresses, passport information, past trips and the notes you keep against a customer normally come over cleanly, because those are simple fields that exist on both sides. If your old records live only on paper, or scattered inside your email, someone still has to type them in, and that part cannot be automated.
There is one honest limit worth knowing before you start. An old booking that is brought in arrives as a record you can read, search and report on, but it is not a live booking any more. It is not connected to the airline or the hotel, so you cannot amend or cancel it from the new system the way you could with a booking made there. Anything still to be changed has to be handled with that supplier direct. How much of the loading we can take on also depends on how tidy your file is and on your plan, so please ask rather than assume.
A good next step is to export a small sample of your current records, even a few dozen rows, and send it across so we can tell you which columns will map straight over and what needs cleaning up first.