A “web application” is, for all intents and purposes, a new application, and should be approached in that manner.

The exact approach will wholly depend on what sort of application it is.   You might be able to build a web application that invokes the existing application – or, more likely, that sends a request from the web-server to some other “application server” to do so.

It is very reasonable to presume that suitable frameworks already exist within Perl/CPAN to do most of these steps.   There are CGI handlers, batch processing schedulers and parallel fork-managers, robust and reliable queues, and so on.

The most serious issue that you are likely to run into, is the bugaboo of all web applications:   maintaining state.   Hence the thought that, perhaps, the process which actually runs your application might not be the web-server proper.