What’s the halacha when one is moving homes within 30 days of Pesach? Does he have to do bedika in the house although he will not own it and will not be renting by the time Pesach comes? The question includes the case when one won’t own a house on the 14th of Nissan.
One who is selling or permanently leaving his house and leaving permanently is exempt from bedikas chametz. He will fulfill his obligation in the house he is living in on the eve of bedikas chametz. Even if he does not own the house, either he [or the one he is staying by on his behalf] will perform biur [searching and destruction] of his chametz.
See Shulchan Aruch O:C 436:3 and Mishna Berura.