Galldrian was an unremarkable ruler for the most part, although not prone to quite the same excesses as his predecessor. He hired many masons, including Ogier, to rebuild the Topless Towers of Cairhien, but eventually stopped paying them for their work, and the Ogier, at least, left the city. Instead, he became obsessed with digging up the giant statue buried in the hillside near Tremonsien - apparently unaware that it was in fact a sa'angreal of unparalleled power, the male half of the Choedan Kal - to be transported to the city of Cairhien as a symbol of his greatness. This might have been possible evidence of him being an unconscious male channeler.
Galldrian, like all Cairhienin nobles, was meshed in intricate plots related to Daes Dae'mar - the Game of Houses, also known as the Great Game. His closest rival was Barthanes Damodred, High Seat of House Damodred and close cousin to the deceased King Laman. His plots eventually caught up with him when he sent strongarms posing as Barthanes' men to question Thom Merrilin about Rand al'Thor. The men killed Thom's lover Dena, and in retaliation Thom appears to have assassinated the king. This sparked a civil war across Cairhien, and no one was been able to secure the Sun Throne for years afterwards. Rand al'Thor took control of Cairhien, but declined to establish himself as King. Instead, he established a stewardship initially under Rhuarc and Berelain, and after them under Lord Dobraine Taborwin, with the project to leave the throne to Elayne Trakand, who eventually took it just before the Last Battle.