In book 20 of Homer's Odyssey, what role does Telemachus play at this point?
This is a great question. By book 20, Telemachus is a different person. The youth of the earlier books is gone. He is now a confident man. This was partially due to his successful mini-journey to see Nestor at Pylos and most of all on account of his reunion with his father.
By book 19, he is preparing to kill the suitors with his father, even if the odds are against them, due to their great numbers. We see Telemachus storing weapons for the day of attack.
When book 20 approaches, we see Telemachus at a dinner with the suitors. He is portrayed in a totally different light. There is little fear, even when the suitors are plotting to kill him. And in one instance, when one of the suitors throws a cow's hoof at Odysseus in disguise, Telemachus responds with harsh words. He threatens the suitor with death. He say that he will run his sword through him.
In the following book, Telemachus will play a pivotal role in the slaying of this suitors, the saving of his family, and the reestablishment of his father.