Objection 1. It would seem that Christ did not have the key. For the key goes with the character of order. But Christ did not have a character. Therefore He had not the key.
Objection 2. Further, Christ had power of "excellence" in the sacraments, so that He could produce the sacramental effect without the sacramental rite. Now the key is something sacramental. Therefore He needed no key, and it would have been useless to Him to have it.
On the contrary, It is written (Apocalypse 3:7): "These things saith... He that hath the key of David," etc.
I answer that, The power to do a thing is both in the instrument and in the principal agent, but not in the same way since it is more perfectly in the latter. Now the power of the keys which we have, like other sacramental powers, is instrumental: whereas it is in Christ as principal agent in the matter of our salvation, by authority, if we consider Him as God, by merit, if we consider Him as man [For St. Thomas' later teaching on this point, Cf. III, 48, 6; I-II, 112, 1, AD 1. But the very notion of a key expresses a power to open and shut, whether this be done by the principal agent or by an instrument. Consequently we must admit that Christ had the key, but in a higher way than His ministers, wherefore He is said to have the key of "excellence."
Reply to Objection 1. A character implies the notion of something derived from another, hence the power of the keys which we receive from Christ results from the character whereby we are conformed to Christ, whereas in Christ it results not from a character, but from the principal form.
Reply to Objection 2. The key, which Christ had was not sacramental, but the origin of the sacramental key.
Source: Summa Theologica (New Advent)