He eventually became the archaeology teacher at Starfleet Academy, where he saw great potential in Jean-Luc Picard, and soon became very close to him, considering him more than a protégé, but the son that he never had, though he had several children of his own who didn't follow in his footsteps, and Picard saw him as more of a father than his own as his relationship with Maurice Picard had ended when he joined Starfleet.
Picard, who also had equal potential to became a great commander and officer in Starfleet, was ultimately forced to decide between going into space as a member of the fleet, or become Galen's archaeology partner on his expeditions. Picard, whose desire to explore space was the ultimate reason for him enlisting, ultimately decided to refuse Galen's offer, leaving him heavily disappointed, and the two lost touch. Galen, nevertheless, decided to remain as Picard's friend and kept track of his career and accomplishments (as Picard did as well for Galen). Galen, meanwhile, continued his career, holding symposiums, working at excavations sites far beyond Federation space, and eventually became the most reknowned archaeologist in the Federation, with his best works being on his studies of the Kurlan civilization.
In 2359, Galen began expanding his research into micropaleontology, where he discovered a four billion year old code programmed into the protein sequences of DNA fragments in dozens of species across the galaxy. Realizing the ground-breaking effect it would have on the Federation and future research into the past, Galen soon began devoting his entire life to the pursuit of additional fragments to complete the code. Galen didn't publish any additional papers, attend symposiums or spend hardly any time in Federation space, mainly spending his time beyond the outskirts of civilization, and his reputation grew due to the shroud of mystery that now surrounded him. (TNG episode: "The Chase")
Later that year, Galen was close to deciphering the code, but wanted to share his phenomenal discovery with his star pupil, Picard, and piloted his personal shuttle to the USS Enterprise-D, where he gave Picard a surprise visit and a Kurlan relic. Galen reconnected with his friend, and asked him to come with him for the remainder of his journey. Picard, whose career in Starfleet was equally prosperous, disappointed Galen by refusing him yet again, and Galen left the ship immediately in anger.
On his way to Indri VIII, Galen's shuttle was attacked by a Yridian destroyer, whose operators wished to supply Gul Malyn Ocett with information on the code. Galen sent a distress call to the Enterprise-D, but his signal was jammed and the shuttle was boarded by three Yridians, who promptly shot Galen point-blank with a disruptor blast, fatally injuring him. The Enterprise-D arrived at that moment, and after destroying the Yridians and stopping them from stealing information, Galen was transported to sickbay. Doctor Beverly Crusher couldn't save him, and Picard came for a final conversation with his mentor and friend. Galen apologized to Picard, and admitted he was too harsh with him, and died. Picard was devastated by the loss of Galen.
Picard, hoping to solve the mystery of why Galen died, soon completed the code, and discovered its secret: the code's program is a message from the Vilmorans, a race of ancient humanoids. They explored the galaxy, but discovered they were the only humanoid life out amongst the stars, and when faced with their extinction, decided to seed humanoid life amongst the primordial seas of hundreds of worlds, including Earth, Cardassia, Qo'noS and Romulus, as their legacy and monument to their existence. This discovery ensured Richard Galen's place in history. (TNG episode: "The Chase")