text: what happens when a senator cannot complete a term?   actually, the governor appoints a new senator. he/she needs no approval from the state legislature. the only thing is that if it is over a year from the next election for that seat, a special election must be held. but if it is less than a year they may serve out the rest of the term. in 2005, new jersey senator jon corzine was elected governor. he was sworn in in january and he had the privilege of picking his own successor for that seat, rep. rob menendez. since the next election for that seat in in november, there will be no special election