So there are three ways i see the transition to part two of the series happening...
Obviously, SPOILERS, obviously
The most reasonable is that Nimue goes to sleep and the narrative jumps forward a hundred years while Safehold culture adapts to the changes in the Church and the relaxing of the Proscriptions. After that hundred years of wait the descendants of all the main characters are ready for Nimue (and Nahrmann =) to help them reveal the truth, ditch the Proscriptions completely, and make another big technology leap forward. This time instead of going through the Age of Sail at warp speed they'd jump into and burn through the Space Age at maximum velocity.
The next most reasonable is that Nimue goes to sleep and the narrative jumps forward ten to twenty years. This would allow most of the main characters to stick around, albeit in a somewhat more mature state, and allow the current crop of kids to join the plot as full-fledged characters. The reason for a ten to twenty year jump could be some contrived reason why they can't deal with the thing under the Temple directly when they conquer Zion, and they need to wait for whatever it is to wake up on its own. Or alternately that they don't think they need to wait 100 years for things to settle down before making the big reveal and jumping from the Age of Steam to the Space Age.
Finally, the least reasonable is that Nimue doesn't go to sleep and the narrative doesn't jump forward at all. In the first five years they've gone from galleys, cannon and muskets (i think?) to galleons, rifles and artillery shells, while they have plans in the works for breach loaders, cartridges, mortars, steam engines and ironclads, all of which will probably be in production within the next year and all of which will be old hat by the time the next five years is up.
So they jumped from about a 14th century level of technology to about a 17th century of technology (with 18th century weapons) in the first five years, and will be at least to a general level of late 18th or early 19th century technology by the end of the second five years. One could argue that at that rate it should only take another 5-10 years to hit late 20th or early 21st century technology, which could easily be covered in real time with no major jumps.
Of course technology has been advancing so fast for the past 100 years that it seems hard to imagine compressing all that down to less than a decade. On the other hand that might just be a bias based on our current perspective. "Well of _course_ they could speed up early technological development, but that's just because our ancestors were slow. But _we_ have actually been progressing at a decent rate, so that can't be rushed through." An alternative argument against the idea would be that the rate of cultural change required for everyone to handle jumping from 14th century tech to 20th century tech within a single generation just isn't reasonable. Trying to make that argument however would probably get one involved in a morass of analysis about how technological development in the third world during the 20th century has or has not gone well.
But in any event, it _seems_ like it wouldn't work, but there's already one demonstrable case where Weber has been in a similar situation and said "damn the torpedoes" anyways. The original plot for the Honor Harrington series was for Honor to die (somewhere around book 11 or 12 i think?) and for the plot to fast forward a couple decades at which point her kids and others of the younger generation would continue things. However the fans got attached to Honor, and Eric Flint jump-started events in the related series he was working on, and Weber decided it was easier to keep her alive and deal with the stuff he'd planned for the far future now instead. Which sounds suspiciously familiar to the way things are going with Nimue and Safehold.