You should actually receive the final Closing Disclosure before you get the final Clear to Close. The CD is the final statement of what the specific terms of the loan will be and does not have to wait for the CTC to be issued.
Additionally, federal law requires a three day period between the issuance of the CD and the actual closing. In many cases, this allows the closing attorney or title firm to draft the closing documents and have them at the ready when the CTC is finally given. I have seen some rare cases where the closing was actually done the same day as the CTC because the CD was issued in a timely manner and the three day period had already passed.