Here is the footnote from the Aquinas Study Bible, though I am in the process of revising it, but here is what I have now
key of David: Rupert of Deutz interprets the key of David to be the knowledge of those mysteries which are latent in the sacred Scripture. Others (Andrew, Arethas, etc.) by the name of the key of David, in this place, have thought that the regal power of David is signified, according to which David in various ways wonderfully prefigured the power and empire of Christ our Lord. Lastly, some there are (St. Ambrosius Autpertus, Haimo) who have interpreted the key of David to be Christ himself as man, or his human nature received from the root of David, according to which he was born, conversed with men, died for man, was raised from the dead, and exalted into heaven, and is set down at the right hand of God the Father, and appointed judge of all men.