How can anyone think the possible end of Sir Patrick's tenure wasn't foreseen by the controllers and other 'powers'? Of course they knew it was going to happen, and soon, just not 'when'.
The first question is whether to continue or end it. We all hope the it goes on but the decision will be down to some media studies graduate of the 1990s with no knowledge or interest in science matters and zero understanding of how much it matters. They'll look at the viewing figures, the cost and may consider the bigger picture including the BBC's public service remit - but mostly the first two.
Assuming it's allowed to continue on similar basis, the decision of who becomes the New Face of SaN is between the current apprentices, not somone else who may have been a past guest. Lintott was clearly being groomed for the position and will be ably supported by the others who have all done sterling work. One or other Brian may turn up from time to time but the central job is most likely to be Chris Lintott, possibly sharing it with some mix of the other three.
....If it's allowed to continue.
If a BBC media studies numpty wants to run it into the ground and trample on Sir Patrick's legacy, they'll either put someone more "media-friendly" (Hammond? a Blue Peter presenter? a non-science but personable and attractive young woman?) or else scrap it but pretend they're continuing within the One Show or other similar brain-dead vehicle and consign it to history.