It's unclear which treatment (there are multiple companies which have developed antibody treatments) Secretary Carson received or why the president would need to authorize it. According to CNN:
When Trump had Covid-19 last month, he received Regeneron's experimental antibody treatment, which is still in large-scale clinical trials but has been available for compassionate use -- something the FDA has to approve on an individual basis, as it did for the President. The company in October applied to the FDA asking for emergency use authorization of its antibody treatment.
It's not clear how the President could have cleared Carson to take the antibody treatment or if Carson got Regeneron's treatment. Eli Lilly, which also makes a monoclonal antibody treatment, declined to comment when CNN asked if Carson had been given their treatment. CNN has also asked Regeneron if Carson received their treatment.
CNN has reached out to the Department of Housing and Urban Development for more information on Carson's treatment.