More from Aquinas:
Psalm 16:
““Deliver my soul from the wicked one”, that is, from Saul, “and from the men of your hand” who have contradicted your hand. . . . According to the Gloss, “Saul” signifies “death”, and just as with the death of Saul, David reigned in peace, so too Christ banished death after the resurrection.”
Psalm 17:
"And this psalm, word for word, is to be found in 2 Kings 22. The story is, as in 1 Kings 19, how Saul sought to kill him: and when Saul had died, 2 Kings 2: Again Abner and his son were against him.
"In the end David was victorious over them. And on this account he made this psalm. And Jerome says the same thing. And since Christ is signified by David, all these things can be referred to Christ, either according to the head, or according to the body, namely the Church, which is liberated from Saul, that is, from death: the name “Saul” is translated as “petition”, because he was given, or rather extorted (from God) because the people asked for him, and he was not given so that he would remain for any length of time.
Here he explains that the typology is sometimes less straightforward:
Psalm 22:
"In the preceding psalms, we saw an earlier act of tribulation which David endured from his son and from Saul; however here, in the third group of ten, the discussion is about the persecution which was suffered by all people, who threw him aside into Saul’s command. . . .
"This very Psalm, among others, treats of the passion of Christ in a spiritual manner. And for this reason, this is its literal sense. Therefore, Jesus referred to this psalm particularly during his passion when he cried out “Eli, Eli, lema sabacthani”, that is, “My God, my God” as begins the psalm. Thus, although this psalm speaks figuratively about David, nevertheless it is especially referred to Christ in a literal sense.
"At the Synod of Toledo, a certain Theodorus Mopsuestenus, who was explaining this psalm literally with respect to David, was condemned, because of this approach, and for many other reasons; he ought to have explained it with respect to Christ. Let it be known this is treated of abundantly before the passion of Christ, of which this very Psalm is the first. . . .
"The discussion in this psalm is principally about Christ’s passion. It touches, secondarily, on the resurrection, because it is given that the passion is to be understood in it, and that the passion is ordered to the resurrection, just as if I were to say that “This slave is freed”, shows that he was a slave. Therefore, the psalm itself is of David, that is, of Christ.
"The title here refers to the time when David was a fugitive, and was hiding in desert places like a stag. Thus, he previously said, And he set my feet as of a stag. Therefore, this psalm itself is entitled for the very tribulation which symbolized the passion of Christ.
“Nevertheless, this mode is referred better to Christ, so that by the stag is understood human nature in Christ, because the stag crosses a thicket of thorns without injury to its foot, just as Christ crossed through this present life without defilement.”
Sorry this was so lengthy. Please do correct me if I am mistaken.
God bless!