Game of Thrones season 8, the show's final season, is comprised of only six episodes, as opposed to the series' standard 10 (with the only other exception being season 7). As such, the show has less time than usual to wrap up every single plot line. With this in mind, it's only natural that several side stories would fall to the wayside in favor of focusing on the central stories involving the Iron Throne, the war against the undead, and Daenerys Targaryen's (Emilia Clarke) decent into madness.
The show's final episode, "The Iron Throne," offers an epilogue to (nearly) every major character's story. However, one key player's arc ends with him in a position that his plotline from the previous season would have made impossible. Perhaps Game of Thrones is implying that he was able to complete this quest off screen during or after the conclusion of season 8's main story.

Samwell Tarly: Maester in Training
After the death of Maester Aemon (Peter Vaughn), Samwell Tarly (John Bradley) volunteers to leave Castle Black and head to the Citadel of Oldtown to earn his chain and replace Aemon as the Night's Watch's Maester. Sam takes his wildling friend and lover, Gilly (Hannah Murray), and her infant son, "Little Sam," and the two depart for Oldtown.
Sam intends to drop Gilly and the baby off at his home in Horn Hill along the way, since women are not permitted at the Citadel, but after his father Randyll (James Faulkner) learns of her wildling heritage, Sam resolves to bring Gilly and Little Sam with him to the Citadel, stealing Heartsbane, the ancestral sword of House Tarly, on his way out.
Upon his arrival at the Citadel, Sam begins his Maester training by taking on menial labor, much to his chagrin. After months of doing very little but scrubbing the floors, Sam is present when Archmaester Ebrose (Jim Broadbent) examines Ser Jorah Mormont's (Iain Glen) Greyscale, determining that he is doomed to succumb to the disease.
However, Sam refuses to give up on Jorah, the son of the previous Lord Commander of the Night's Watch, Jeor Mormont (James Cosmo), who took Sam under his wing, so Sam performs a risky procedure to cure Jorah, who leaves the Citadel healthy and able to rejoin Daenerys' forces.
However, Ebrose punishes Sam for going against his orders, forcing him to sift through old scrolls. While looking through these scrolls, Gilly accidentally discovers that Prince Rhaegar Targaryen (played by Wilf Scolding in flashbacks) secretly had his marriage to Elia Martell annulled. Not long after this revelation, Sam leaves the Citadel, frustrated that the Maesters refuse to take the threat of the undead invasion seriously, and returns to Winterfell, swiping as many scrolls as he can carry.
When Sam arrives at Winterfell, he and Bran Stark (Isaac Hempstead-Wright) piece together Jon Snow's (Kit Harington) true parentage, combining Bran's magic and Sam's knowledge: Jon is actually Aegon Targaryen, the legitimate son of Prince Rhaegar and Lyanna Stark (played by Aisling Franciosi in flashbacks), and the rightful heir to the Iron Throne.
This discovery, along with curing Jorah, is the main narrative function of Sam's time at the Citadel, since he never returns to Oldtown throughout season 8.

Grand Maester Sam?
The series finale sees Sam as a member of King Bran's small council, alongside several other fan-favorite characters, including the new Master of Ships, Ser Davos Seaworth (Liam Cunningham), the Master of Coin, Ser Bronn (Jerome Flynn), the Hand of the King, Tyrion Lannister (Peter Dinklage), and the Lord Commander of the Kingsguard, Brienne of Tarth (Gwendoline Christie). As for Sam, his role on the council is that of Grand Maester, succeeding Pycelle (Julian Glover).
However, based on Sam's season 7 storyline, he should not be able to serve as Grand Maester, since he never even became a Maester. Sam left the Citadel before finishing his studies and forging his chain. While Sam is far from the least qualified member of this council (Bronn, the Master of Coin, once needed the concept of debt explained to him), as it stands, it is unclear how Sam is able to hold this position.
Perhaps Bran was able to make an exception to allow Sam, his confidant, to fill the role, similar to how Cersei (Lena Headey) utilized Qyburn (Anton Lesser) to fulfill the duties of Grand Maester after Pycelle's death, despite his expulsion from the Citadel.
Or maybe Sam was able to complete his studies after his bravery during the Battle of Winterfell, likely earning a little more respect along the way. Additionally, King Bran could have pulled a few strings as the ruler of the Seven Kingdoms to allow Sam back into Oldtown despite his abrupt exit.
Regardless of how it happened, it is satisfying to see Sam fulfill his dream of becoming a Maester at the tail end of the series.
