Security Clearance Crossover (Govie to Contractor)

Good afternoon

I’m currently canvassing for potential opportunities outside of my government agency. I have found a potential opportunity that I may take.

My clearance is currently housed in scattered castles and the contracting job requires my clearance to crossover to scattered castles. Therefore, I would assume there wouldn’t any issues.

Is this correct?
Also, will my government agency be notified that a company has intiated the clearance crossover process?