In the Eastern churches, not having a beard for clergy is a no-no.
At one time, in Russia especially, the beard was an outward sign that one was a . . . Christian.
The Lithuanian martyrs, Sts Anthony, John and Eustace of Vilna, were killed by the pagan prince Oldgerde for refusing to shave their beards.
The Russian Old Believers were persecuted by Tsar Peter I for the same thing and they had to pay a tax for the right to wear a beard.
The beard in our tradition reflects Christ Himself and the beard He wore. Since we (and clergy especially) are called to be an “Alter Christus” (sorry for that Latinization!), they wear beards and long flowing robes etc.
In some quarters of the Eastern Church, to have short beards is already suspect . . .
There is a (true) story of a North American Greek bishop going to Mt Athos. Seeing his short beard, the monks there chided him and told him to stand in the back of the church for the All-Night Vigil Service (which means they pray all night, of course . . .).
The bishop did so and stood alone in the back, praying and singing the hymns.
By morning, a saintly monastic elder came by and asked the monks at the front who the man in the back was over whose head he kept seeing angels suspended in mid-air . . .
When told that he was a bishop sent there for having a short beard . . . the monastic elder chided them and said, “What have you done to that holy man?! You know, throughout the night I kept seeing dark figures hovering over your heads!!”
The symbolism of the beard is also contained in Psalm 133: “Behold how good and how pleasant it is for brethren to dwell together in unity. It is like the precious oil upon the head, running down on the bear, the beard of Aaron . . .”
Alex