Rience is a mage of considerable skill who is sent after Ciri in the novel "Blood of Elves". He is not as powerful as his master, Vilgefortz. In his quest to find her, he captures and tortures Dandelion to get information. If not for the extremely timely intervention of Yennefer, Dandelion might not have survived to continue his role as Geralt's frequent companion.
Yennefer's rescue of Dandelion leaves a permanent "impression" on Rience. While the mage does manage to escape with his life, the sorceress' final spell leaves the left side of his face permanently disfigured. Making him rather easier to track.
According to Codringher and Fenn, Rience's endeavors to seek out Ciri were all in an effort to prevent her from becoming a wife or mother, as such a fate would prove dangerous were she to fall under the wrong influence.
Rience dies while pursuing Ciri across the frozen surface of Tarn Mira. When the young witcher attacks his party his own spell misfires and breaks the ice beneath his feet. Almost submerged in the freezing water he clutches the ice for his very life when Ciri skates through his fingers, severing them and leaving him to drown in the lake (in a cruelly ironic retaliation for his previous threaths abouth the things he would do to her "with these very fingers").