TL;DR: Skip this reply if you don't have NEXUS clearance, but if you do, please read on...
There is a "but", here - if you have NEXUS (such as I do), you /do/ need to tell them about the new passport (just as you would have if you had gotten or renewed a Canadian PR card.) Go through the usual portal access and it's relatively straightforward to add it.
CAVEAT: NEXUS has apparently cracked down on their process to renew their cards (thankfully, they've automatically extended the validity by quite a bit both to offset the new paperwork in addition to COVID) - you'll have to spend about an extra 15 minutes or so filling out onerous paperwork if you haven't logged in in awhile.
Good luck.