website does not work with the latest wordpress update

Hello, we have our website (peruagency.com), but it does not work correctly with the latest version of wordpress. since I think it only works with jquery 1.12.4, and my wordpress is in v3. What should I do, since I want to update to use plugins like jetpack and since I have errors with contact form 7 about some refill, since they require that everything be updated to the latest version.
what should I do or what has to be done.