To change from HTTP to HTTPS requires the client to make a new connection, as it will need to perform a SSL handshake. With Apprules you can force the client to reconnect to a HTTPS enabled cluster, which would be best done using a redirector. You can use apprules to issue a redirect to HTTPS like:
If you want to re-write the server responses which contain links to http:// so they are sent as https:// the above PDF has an example of how to do this, like:
PTC: content contains "http://" then replace content term "https://"
It is also suggested to re-write Location headers which are sent in redirect (3xx) responses like:
PTH: reply_header "Location" contains "http://" then replace reply_header "Location" term "https://" and continue
The PDF has more examples for PeopleSoft where the cookies, Referer headers etc are all checked and replaced which can be used to create your own rules. If you inspect the content returned, you should be able to craft apprules to re-write any content you find that contains incorrect links.