Hi Derek,
We don’t have any tools for this so it’s going to require a custom approach at this time.
I’m guessing you/they don’t want to move the event data across manually – but perhaps some code could be set up on this external site to read in event data either via The Events Calendar’s ical feeds or by some good old fashioned “screen scraping” (less ideal, but still viable).
Does that help at all? I’m afraid it’s not an area where we can go into too much depth, given that it is custom development territory.