One Trinitarian answer is explained in the Church Grammar episode Tough Christology Questions minute 25:28-31:47 on the relationship between Christ's divine and human life.
Jesus here is apparently saying the Holy Spirit doesn't know something. How do Trinitarians, who hold the Holy Spirit as a co-equal person of the Godhead, understand this verse?
Dual nature of Christ (posited by the 3rd council of Constantinople that there are two operations and two wills in Christ) makes it easy: the Holy Spirit (and the Eternal Son) knows, but who from eternity does not inspire the human Christ (a time-bound fleshly "extension" of the eternal Word) to reveal that information to us. Thus in his human nature Christ didn't access that knowledge. With this understanding:
- The wording "no one knows" means "no created being knows", including the human nature of Jesus.
- "nor the Son" means "nor the Son of man" (in all other instances in Mark Jesus uses "Son of man" to refer to himself), thus implies the human nature of Christ, not the eternal divine nature of Christ. The Amplified Bible translation makes it explicit:
But of that [exact] day or hour no one knows, not even the angels in heaven, nor the Son [in His humanity], but the Father alone.
What is the justification of the above reading? In the Church Grammar episode, Thomas J. White pointed out 2 kinds of knowledge that Jesus has, some of which can NOT be known from his human nature alone (such as knowledge of his own identity), but some which can be known only by prophetic grace when the Holy Spirit reveals the information to Christ's human nature.
BUT the wording of Acts 1:7 (Jesus's answer to the disciples question "Lord, are you restoring the kingdom to Israel at this time?") on the same topic as Mark 13:32 / Matt 24:36, which says "it is not for you to know the times or the seasons ...", implies that Jesus knows some things that he was NOT sent to reveal. So in Acts 1:7 we can deduce that the Holy Spirit didn't impress the human Jesus with this prophetic knowledge since it is not needed for our salvation.
Fr. Thomas White pointed out the pedigree of this reading from the 6th century:
One classical way of reading this goes back to Pope Gregory the Great who was also a theologian of some profundity in the sixth century [which] is to say that the things [Jesus] claims not to know he reveals elsewhere as things he has not been sent to reveal.
CONCLUSION: The Holy Spirit knows, and the Father and the Son who is consubstantial with the Holy Spirit must know also. But in his human nature, Jesus either doesn't know or doesn't want to reveal this knowledge.