Consultant role ended and clearance in process

My employment ( I am a consultant) just ended but accepted an offer from a government contracting company in December last year.

I am currently waiting on clearance and my current employment (consultant at a company) just ended ( completed the project). I am currently looking for another contract or temporary work while I wait for my clearance to be processed.

Should I tell potential employers about the company that offered me a job, and that I am waiting on my clearance or just keep quiet about it? I don’t want to lie about it.

If potential employers know that I have already accepted an offer will they hire me in any case? If I don’t tell the potential employers and I am hired, how will it affect my reinvestigation?

Please advise.