Ser Jaremy attends the induction of new recruits into the Night's Watch. He is the acting first ranger in the absence of Benjen Stark and summons the recruits assigned to the rangers after the Lord Commander's speech. He leads an escort for Jon Snow and Samwell Tarly when they go north of the Wall to take their vows in the Godswood. He embraces his newly sworn brothers after they take their vows. They discover the bodies of rangers Othor and Jafer Flowers near the Godswood and return them to Castle Black. The dead men had accompanied Benjen on his scouting mission beyond the Wall.
Ser Jaremy and four other men were killed by the wight Jafer Flowers. Jaremy managed to hack the wight's head off, but was killed when the headless corpse pulled his own dagger from its sheath and buried it in his bowels.
Give that Ser Jaremy is not shown to be killed in the episode, it is possible that he simply wasn't killed in the TV continuity.