The Shulchan Aruch (551:10) rules that one may not eat meat or drink wine during the nine days unless it's a Seudas Mitzvah.
Included in the list of what's considered a Seudas Mitzvah is making a siyum.
What is the source of a siyum being a Seudas Mitzvah? Can one make a siyum during the nine days even if he finished his learning earlier? To eat meat when it's typically forbidden, he saves a part of the tractate for the siyum during the nine days.
The Shulchan Aruch in Yoreh Deah (246:26) rules that when one finishes a tractate, it is a mitzvah to rejoice and make a meal called a Seudas Mitzvah. This is based on Gemara Shabbos (118b), which says: "Abaye deserves a reward because when he sees someone complete a tractate, he makes a feast."
Many Acharonim, including the Elya Rabbah (551:26), Aruch HaShulchan (551:28), Chai Adam (133:16), and Mishna Berura (551:73), rule that one should not plan to complete his learning during the nine days.
He should not speed up or leave over a part to eat meat during this time.
However, Kaf Hachaim (551:161) cites Moed Katan (9a) as proof that one could postpone completion until the right time (Aruch HaShulchan argues on the proof).
In practice, the custom is always to make siyumim during this time, whether he finishes it at his regular pace, slows it down, or quickens his learning.