In JQS1, Carrow starts as a Cleric of Vieris gifted with healing magic. He uses this healing magic on Perf after Perf is beaten by Glorion, but quickly into the season, Carrow is shot by three orc bowmen at Rilk's order. He dies. Nara orders Perf to heal Carrow, but Perf's retromancy turns him undead instead.
As a sentient corporeal (revenant), Carrow assists Perf and Nara as they battle the orcish warparty. They are soon captured by the Assassin.
In JQS2, the Assassin takes Carrow and the others through Sumber, the City of the Dead. Carrow tries to turn undead using his holy symbol, but he looks at it and accidentally turns himself. After running, he comes face to face with the Pale Lady, Death. Carrow denounces her and calls upon Vieris, but his arm explodes.
He again calls upon Vieris to deliver them from the assassin. Vieris sends an angel who turns on Carrow and destroys his holy symbol. Strong like Bull labels Carrow a death priest and asks him to imbue a horn with shadow to defeat the angel's protective aura. To save Perf, Carrow does. He and the others are recaptured by the assassin, but Carrow chews off his own arms (one being the angel's) to free himself.
In JQS3, (Incomplete)
Description from Dead Gentleman Wiki: At the start of the series, he is a Cleric of Vieris, a God of the Light, and is the quest group's healer. He is killed in a surprise attack by Orcs after rushing to warn Perf of the possibility of an Orc attack. Perf attempts to revive Carrow with the "Breath of Life" spell, but it goes wrong. Carrow reawakens as a completely new type of undead: corporeal (has a physical body, which is of course a rotting corpse), yet with a soul that retains its memories and intelligence. His newfound undeadness has huge consequences for his position as a Cleric. Despite his continued faith in Vieris, spells meant to repel evil or undead beings also begin to affect him, and an archangel of the Light attempts to slay Carrow after being summoned by the undead cleric. His personality also seems to have changed upon his transformation into an undead. Where before he tried to convince Glorion that killing Orcs was not necessary, after his change Carrow showed no compunction in killing and eating Orc (he later spat the Orc meat out of his mouth, with an exclamation of disgust). Death also takes an interest in Carrow, and it is hinted that he feels nothing or next to nothing. Strong Like Bull at one point calls Carrow a death priest and asks him to imbue an object with shadow.
During the second season, Carrow loses his right arm after using a holy symbol of Vieris to banish Death (this might have failed, as after his arm explodes nothing more is seen of Carrow until he rejoins the party). He replaces it with the right arm of an archangel slain by Perf and the Sword of Fighting (Carrow helps them here by using a shadow-imbued object to remove the nimbus of the archangel, for which Death applauds him), though he is reluctant to admit this. Later, near the end of the series, he escapes being bound by tearing off both arms and undoing Nara's restraints with his teeth. After the fighting is over, he reattaches his arms. The method he uses to attach the arms is unknown, but presumably he just holds them to the stump of the limb and they automatically reattach, though how that worked with the archangel's arm, who knows?
Becoming undead is quite a shock for Carrow. He states several times that he is not a zombie/undead/monster, though other servants of the light view him as one, and holy spells meant to repel evil of the undead also affect him (wait that was mentioned already wasn't it oh well moving on). Death comments that he is progressing faster than she thought, though what he is progressing towards is unknown.