For once the questionable anonymonk is actually right: the problems do not start immediately, but over time you can accumulate multiple different frameworks into the larger application. Unless you have full management buy-in that all future work on the application is to use framework X, do not think that you are starting an "incremental" conversion to move the application to framework X. That way lies the madness of an application with parts in framework A, parts in framework C, parts in framework X, parts in framework R, and an unmaintainable mess on the whole.
You can still use newer modules like Template for newer features, especially if you can rally support for refactoring the existing code to also use Template, which will help set you up for a later move all-at-once to a more modern framework, after a destination framework is chosen. Right now, your application uses the (very minimalist) "CGI" framework and you should not take changing that lightly unless you know that you will be able to change the entire application to a new framework. Multi-framework applications are maintainability nightmares.