John Chrysostom

The reason, however, why the Lord told them this, was to show, that after His cross and resurrection, Christ must be preached by His witnesses. Again, Peter alone, from the fervour of his disposition, had the boldness to dispute about these things. Wherefore it goes on, And Peter took him up, and began to rebuke hime.

Catena Aurea by Aquinas ↗

Theophylact of Ohrid

The Lord commanded them to tell no one, because He wished to conceal His glory, lest many be scandalized by Him and, in their unbelief, become liable to greater punishment.

Commentary on Mark ↗

Bede

And he warned them not to tell anyone about him. And he began to teach them that the Son of Man must suffer many things, and be rejected by the elders, the chief priests, etc. For this reason, he did not want to be proclaimed before his passion and resurrection, so that afterward, when the sacrament of his blood was completed, he could more appropriately say to the apostles: "Go and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Spirit." Because it would not benefit to preach him …

On the Gospel of Mark ↗