Why do we kiss the hand of the bishop or priest after Divine Liturgy?
We are not showing respect to the person of the priest but to his sacred office. The priest as a man is a sinner, but the priest as priest represents Christ; he is an icon of Christ.
Although his hand is unworthy, yet it touches the Most Holy Things-- the Precious Body and Blood of the Lord.

Despite his unworthiness, in Holy Ordination he has received the Grace of God to impart spiritual gifts and blessings.
Why would we deprive ourselves of the blessings of our Lord Himself, by not seeking the priest’s blessing?

So when would we ask for a blessing?
We typically seek this blessing whenever we greet and bid farewell to our spiritual fathers.
Also, we kiss their right hands when we receive the prayer of absolution at confession or at other prayers.

Glory be to God

Glory be to His Virgin Mother

Glory be to the Holy Cross