Clearance Crossover Process

I’m currently in the process of obtaining a part time job which requires an active security clearance. I recieved my conditional offer contingent of clearance crossover from my current employer. My question is, will this interfere with my clearance being held by my current employer and cause issues? Am I safe to assume that my curremt employer will maintain my clearance and the employer that’s crossing my clearance over will just be added as some sort of subsidiary?

You a contractor? If so they are just signing on to the JPAS clearance.

I’m a government employee looking at PT for a contractor