Recruitment

The narrator of Robert Heinlein's "All You Zombies -" recruits himself to the Temporal Bureau.

James Blish's "Beep"/The Quincunx Of Time ends with the Service about to take in a new raw recruit.

Poul Anderson's "Ivory, And Apes, And Peacocks" ends when Manse Everard recruits Pummairam to the Time Patrol:

"'You'll go to the Academy, elsewhere in space and time. There you'll spend years, and they won't be easy years - though on the whole I believe you'll revel in them.'" -The Time Patrol (New York, 1991), p. 203.

Anderson's "Esau" ends when Nicholas van Rijn promotes Emil Dalmady from factor to entrepreneur on 90% commission:

"'...you must have a while in an entrepreneurial school I got tucked away where nobody notices...mainly I think you will enjoy your classes, if you don't mind working till brain-sweat runs out your nose.'" (The Van Rijn Method, p. 552)

Van Rijn cannot hide his school in The Oligocene like the Time Patrol but I bet he can hide it good.

And Blish wrote an appropriate conclusion for this post:

"'Every end,' Wagoner wrote on the wall of his cell on the last day, 'is a new beginning.'"
-James Blish, Cities In Flight (London, 1981), p. 129.