Do I need a ground for a new 240 volt 20 amp circuit?
If you're in the United States, a grounding conductor is defiantly required for all new work. 

If the system was installed before grounding was required, you're not required to update the system and add grounding when the code changes. However, if you add anything to the system after the code change, you must do so in a code compliant manner.  This might mean bringing the entire system up to current codes, or at least enough of it to allow the new work to be code compliant. 

You might be able to simply install a proper grounding electrode at the building, and use that to ground the circuits on the secondary side of the transformer. You'll have to contact your local government to find out if that's adequate, and also to have the work inspected to insure it's done properly.