The Norse High Priest was call a Alsherjargod. Gyðja was the word used for the female priestess.
The Norse priesthood never took on the famous roles of the Celtic Druids. This was because their Norse shamanistic tradition was maintained by all women, called Volvas. The Kings seemed to have instead evolved out of a priesthood style office, like the Celts who had Kings as the head of a smaller group of families in the kingdoms (for this social structure, that is parallel to the Celtic structure. The Kings were like Norse Priest Chieftains.
The Norse priests also had sacrificial burials where slaves and wives as well as weapons and riches and animals would be killed with the King. There is an account where a woman slave volunteered to joined the corpse of a man on the funeral pyre so she would become the man's wife in the next world, an obvious increase in her status.
Most of the existing records on Norse mythology date from the 11th to 18th century and are no less tainted by Christianity then the Celtic myths. In fact even the religious worship of the Blot, resembles that of the Celts.
Here is a poem about a Norse Priest from a medieval Norse version written about 1225 by Snorri Sturluson;
Henry Wadsworth Longfellow
SHORT of stature, large of limb,
Burly face and russet beard,
All the women stared at him,
When in Iceland he appeared.
"Look!" they said,
With nodding head,
"There goes Thangbrand, Olaf's Priest." All the prayers he knew by rote,
He could preach like Chrysostome,
From the Fathers he could quote,
He had even been at Rome.
A learned clerk,
A man of mark,
Was this Thangbrand, Olaf's Priest.
He was quarrelsome and loud,
And impatient of control,
Boisterous in the market crowd,
Boisterous at the wassail-bowl,
Would drink and swear,
Swaggering Thangbrand, Olaf's Priest.
In his house this malcontent
Could the King no longer bear,
So to Iceland he was sent
To convert the heathen there,
One summer day
Sailed this Thangbrand, Olaf's Priest.
There in Iceland, o'er their books
Pored the people day and night,
But he did not like their looks,
Nor the songs they used to write.
All this rhyme
Is waste of time! "
Grumbled Thangbrand, Olaf's Priest.
To the alehouse, where he sat,
Came the Scalds and Saga men;
Is it to be wondered at,
That they quarrelled now and then,
When o'er his beer
Began to leer
Drunken Thangbrand, Olaf's Priest?
All the folk in Altafiord
Boasted of their island grand;
Saying in a single word,
"Iceland is the finest land
That the sun
Doth shine upon!"
Loud laughed Thangbrand, Olaf's Priest.
And he answered: "What's the use
Of this bragging up and down,
When three women and one goose
Make a market in your town! "
On poor Thangbrand, Olaf's Priest.
Something worse they did than that!
And what vexed him most of all
Was a figure in shovel hat,
Drawn in charcoal on the wall;
With words that go
"This is Thangbrand, Olaf's Priest."
Hardly knowing what he did,
Then he smote them might and main,
Thorvald Veile and Veterlid
Lay there in the alehouse slain.
"To-day we are gold,
Muttered Thangbrand, Olaf's Priest
Much in fear of axe and rope,
Back to Norway sailed he then.
"O, King Olaf! little hope
Is there of these Iceland men!"
With bending head,
Pious Thangbrand, Olaf's Priest.