You might be able to arrange conditional hire - meaning you don’t give proper notice to your current job until the clearance is adjudicated then give the proper notice and start the new position two weeks later. Employment hiring is a negotiation process- the future employer doesn’t have a one way street to maneuver through. Protect your current standing without taking chances.
Now that said, realize your current employer will be contacted so keeping the potential job change on the down low is not possible.