The real Alcor perceived the girls in the Arcturus Forest and alerted Ursula.
Akko is introduced to Alcor when she visits Ursula's room to inquire about her "past" with Chariot. Akko does not know that Ursula's familiar is named Alcor, like her plush toy of Chariot's familiar.
Alcor was called by Ursula to bring the Shiny Rod back to Akko. Ursula can also project her voice through Alcor.
Alcor is a loyal familiar to Ursula. She can call him to assist her by whistling. Alcor also informs her about strange events that he perceives.
Akko has a plush toy version of Alcor, and it's one of her most beloved possessions. Akko first met Alcor in Blue Moon and it seems the latter has a particular liking towards the former.