Depending on how you wrote your CLIPS code -- in particular, whether you used the CLIPS object extensions or CLIPS generic functions (neither of which exist in Jess) -- you may be able to run your code directly in the Jess engine with little or no change. The best thing to do is probably to just try it, and see how far you get.
Both CLIPS and Jess are quite flexible systems as far as integrating with other software. Jess is obviously very easy to integrate with all Java-based systems, and there are CLIPS bindings for Python and other languages that are easy to use on the Web. So even if you decide to stick with CLIPS, you shouldn't have any problems creating a web-based application.