No idea Pete.
The logical course of action to me would be for the GOP governor to name a GOP appointee to the seat. It would also make sense for said appointee to be able to retain the seat when election time comes around.
But what do I know?
The last time a similar scenario fell on a NJ Governor was in 1982 when the corrupt Democrat Harrison Williams was forced out of the Senate (due to Abscam). The Governor was Tom Kean, Sr. Rather than appoint someone who could hold the seat for the general election (such as Congresswoman Millicent Fenwick, who was already in the running), Kean went with a seatwarmer in Nicholas Brady (Bush, Sr’s future Treasury Secretary). Lautenberg ended up beating Fenwick (arguing she was, at 71, too old (!) to serve in the Senate). The GOP has not won a Senate race in NJ since ultraleftist Clifford Case won his final term in 1972.