I only remember
this promo, but it doesn't appear to show the scene you're looking for.
I remember that one. Wasn't that the one tacked onto the video of
Star Trek IV, too?
It's interesting to look back on. After "introducing" Captain Picard and Riker, Dr. Beverly (and her brilliant son, Wesley) are next. Was that just following the Kirk/Spock/McCoy-type dynamic? Was she intended to play a bigger part in the show originally?
Then they run through the other characters, and only Worf gets a line. I wonder why that was?
Along these lines, the show's opening credits are pretty interesting, too. After Stewart and Frakes, the rest are listed alphabetically. It works out well, what with Wil Wheaton bringing up the rear. Suppose his name had been, say, Wil Barnes, which would put him before Levar Burton?
Fascinating how sometimes things just work out.
As far as my original question, the more I think about it, it must've been a clip from
Entertainment Tonight, which was covering the pre-release stuff.