Just check for updates in the settings (it's in the "About" menu on my HTC One). If there is an update available for the phone it will tell you there, and you can download it over WiFi. No need to use HTC Sync, which I don't think is used for updates (at least from HTC's description - I've barely used it myself).
If no update is available - which is quite likely with a phone that old - the only way of upgrading further is by rooting and installing a custom ROM. If you wish to learn more about this, we have more information in Desire Z - All Things Root - Android Forums. It is a good idea to make sure you understand what you are doing before attempting this, so if that interests you I suggest registering so that you can ask the people in that forum any questions you might have.
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