Xakic is incorrect. After creation, any new HQs you get, either through recycling or getting an increased member count get added as a use in construction. So when one of your members goes to build a facility, the HQ will be available as a 1 time use (per DC unlock you have) to build.
Also, I presume you have gotten to the next member count threshold to get one - if I remeber correctly you should get a faction event informing you that there is a DC use ready.