I think it should be simple - do you know where you are importing jquery? it is probably just a link in the head section and you probably can just find the newer version url and swap it out. If it doesn’t work undo it.
While I don’t have a lot of jquery experience my guess is there would not be anything that breaks - newer versions would just have new features and fixes but it should work the same. And if you have 1.4 and just need to go to 1.6.3 or the last one in the 1.x family that should not be a big deal. Going to 2.x or 3.x might be more of an issue.
That said you can normally do things in normal JS that jquery was needed for in the past though I’m sure there a zillions of cool things that still rely on jquery.