Have tried to install the AirPort Utility Ver 6.3.1 but I receive an error that the version of my OSX on the system is not supported? Does a newer version exist?
It appears as if you may not aware that AirPort Utility is part of the Mac operating system. So, if you install a new operating system, a newer, more up to date version of AirPort Utility will automatically be installed at the same time as part of the process.
You already have the most up to date version of AirPort Utility installed on your Mac right now. Look in Finder > Applications > Utilities > to find AirPort Utility.
If you want to see which version of AirPort Utility is now installed, open AirPort Utility, click on the AirPort Utility menu in the upper left corner of the screen, then click About AirPort Utility. You will see that you have AirPort Utility 6.3.6......which is a much more up to date version than AirPort Utility 6.3.1 which you may have thought that you needed to install separately.