Did your old work permit expire? Both will likely have expiration dates that match the expiration date of your old work permit. If your old work permit expired, then both will have expired and you have to renew them.
Otherwise, I think you can wait until the expiration date (of course, I mean before they actually expire), or "renew" them now with the new work permit. I don't think they actually care about the different employer, just that there is no gap between work permits...
(which reminds me of a ludicrous "failure to communicate" with OHIP - they insisted that because I had a new work permit (same employer), I had to do the 3-month waiting period over again - it seemed that their brand new computerized system had not been designed to include the possibility of a work permit renewal, it treated all TWPs as "new." It took me 20 minutes and 2 persons up the management chain to get the obvious across - that since my old permit hadn't expired before my new permit was issued, there was no "gap." Two months go by, no OHIP card, so I called them and they then inform me that I had been denied because because my old permit had by that time expired
Fortunately, before I lapsed into a full-blown American-style aggrieved customer rant, I got transferred to a kindly competent person who fixed it...