The name Anastasia does not appear either in the Russian chronicles or in the Hungarian chronicles, where she is referred to as “the daughter of the prince of Russia.” It is mentioned only in such a late source as the “History of Poland” by Jan Dlugosz (XV century), so this name can be considered conditional.[1]wikipedia

cycle “Kyiv princesses on the thrones of Europe, Main Post Office of Kyiv, 2016
Anastasia and Andras I
In 1046, András returned to Hungary with Anastasia and became king after seizing the throne. The Queen founded several Orthodox monasteries in Hungary.
In recent years, Andrash was paralyzed, and Anastasia was increasingly involved in governing the country. In 1060, Bela raised an uprising against Andrásh and in the same year defeated brother. Shortly after which Andrash died, and on December 6, 1060, Bela became the Hungarian king.

Miniature of the 14th century.
Life in exile and the return of the throne
Solomon was declared the new king. In gratitude for the help rendered to her, Anastasia presented the Bavarian Duke Otto of Northeim with the “sword of Attila” – a Hungarian royal relic – which, according to legend, belonged to the leader of the Huns.
With a young son, Anastasia ruled the kingdom, and their position remained precarious, there was an actual dual power in the country. The support of her and King Solomon was Henry IV. The sons of Bela I, Geza and Laszlo, were supported by Poland, as well as the brother of Anastasia, Prince of Kyiv Izyaslav Yaroslavich, who was married to the Polish princess Gertrude.

(Art. Orlai Petrich Soma, 1857)
Anastasia at this time remarried the German Count Poto. It is known about her disagreements with her son. There is a legend that Anastasia cursed him because he put his interests above the state and violated the peace treaty with his cousins. In 1074, it came to the point that Solomon raised his hand against his mother. In the same year, the sons of Bela I Geza and Laszlo overthrew Solomon, who fled to Germany. Anastasia also went there.
Death
Anastasia died no later than 1094, since in this year she is already mentioned as dead. According to legend, she died in the monastery of Admont or Agmund, in Styria. In a number of obsolete studies, the name of this monastery was taken for her name, so that the queen is erroneously called “Agmund” in these works.
On the top of the mountain next to Lake Balaton, near the Tihany Abbey Church, a monument to King András and his wife was erected in modern times. There is an inscription on it: “King Andras I and Queen Anastasia – Ukrainian princess.”
The fate of Anastasia’s children
Sholomon (Solomon)
Having fled to Germany, Sholomon, with the help of the military support of the German emperor, managed to retain the northwestern part of the country. He kept these lands constantly fighting with his brothers, until 1081 – then Henry IV had no problems with the Pope and he refused to give military assistance to Solomon. Because of this, the son of Anastasia was forced to capitulate, receiving in return the forgiveness of his cousin Laszlo I, who became king of Hungary after Geza I.
Returning to court, Solomon tried to plot against his cousin, but was discovered and imprisoned in 1083. In the same year, King Laszlo forgave Sholomon for the second time on the occasion of the canonization (August 19) of Istvan Arpad, the first king and baptist of Hungary. Once free, Sholomon again tried to call for help from his brother-in-law emperor, but was refused.
Then the grandson of Yaroslav the Wise joined the horde of the Pecheneg Khan Ketteshka, who roamed the territory of present-day Moldova. Although his wife Judit was alive and the couple were not divorced, Sholomon married Köteshk’s daughter, thus becoming a bigamist. Promising to give the khan Transylvania, Solomon invaded Hungary from the east in 1085, leading the Pecheneg horde. King Laszlo I met and completely defeated the troops of Köteshk near Kisvarda (North-East of modern Hungary). Solomon again had to flee. He died two years later, in 1087, at about 35 years old, in one of the battles between the Pechenegs and the Greeks.
David
In addition to the elder Sholomon, Yaroslavna had another son, David (1053/1055-1094). However, historians do not know anything about his participation in the turbulent political life of Hungary and the equally turbulent life of his brother Sholomon. According to indirect signs, David became a member of a spiritual order from an early age. There are references to his large donations to various religious organizations, in particular, to the abbey of Tihany, which was founded by his father and mother. Like his brother, David did not leave behind any children, and thus, with his death in 1094, this branch of the common descendants of the Arpads and Ruriks ended.