The easiest way is to re-run Configuration Wizard again on the QC Server (keep settings, choose to point to EXISTING qcsiteadmin DB), then on the ''Application Server'' page, indicate your new port (make sure nothing is using it first), continue the wizard and allow it to DEPLOY and then Start the ALM service.
Your QC Server should now be service on the NEW port.
If you indicated port 80, you don't need a port designated in your QC URL, but other ports will require explicit designation example:
http:// ((your-server)) : ((port)) /qcbin
If you cannot find the link for Configuration Wizard on your QC server, see this article: