Ser Hugh is a freshly made knight. He is killed by a splintered lance while jousting with Ser Gregor Clegane.
Hugh served as Lord Jon Arryn's squire for four years before Jon Arryn's death. After Arryn's death, Hugh was knighted for his loyal service by King Robert Baratheon. When Lady Lysa Arryn returned to the Eyrie with her son, Ser Hugh elected to remain in King's Landing in the King's service.
Lord Eddard Stark sends Jory Cassel to quiz Ser Hugh about Jon Arryn's death. Ser Hugh refuses to talk to Jory since he isn't a knight. Ser Hugh takes part in the tournament to celebrate Eddard's arrival and is killed by a splintered lance during a joust with Ser Gregor Clegane
Lord Commander Barristan Selmy stands the knight's vigil for Ser Hugh overnight. Eddard ponders how Hugh could afford arms and armor so soon after being knighted, leading him to suspect that Hugh was involved in Jon Arryn's death. Varys later agrees that this is the most likely explanation, and that the Lannisters ordered him killed to prevent him talking (Ser Gregor is in the Lannister's service).
Ser Hugh was once a squire to Jon Arryn and knighted by King Robert. Gregor "The Mountain" Clegane killed him in a joust at the Tournament of the Hand before Ned Stark could speak to him about Lord Arryn's mysterious death.