Canon Background
https://awoiaf.westeros.org/index.php/Jon_Arryn

In-Campaign
Jon treated with Theodore Jasper and the young lord’s Maester the morning after he wed Lysa Tully. After Teddy’s diplomatic success in winning House Corbray, House Whent, and House Cox to Robert’s cause Jon saw fit to task the young lord with a more difficult object. Jon explained that if a lord of the Reach would turncloak the rebellion would benefit greatly from their knowledge. Teddy and his companions set forth bound for the Arbor intent on turning the powerful Redwynes.

In the company of Nestor Royce, Jon Arryn made a lordly progress throughout his domain, arriving at Snownook in March of 284 AC. He was entertained by members of the household in various ways, including: a battle of wits, a sparring exhibition, song, a tale of his house’s formation, and a flag capture melee. He shared with House Jasper that he would be naming a Warden Of The Fingers & The Isles and that the house would be taking on a ward, Berta Rowan.

In 284 AC Lord Arryn returned to Snownook to preside over the trial of Ser Gyles. The knight was alleged to have broken his oath as a knight by setting fires to farms and scattering flocks and herds. After hearing testimony Jon Arryn rendered a verdict of guilt and sentenced him to death; when the knight requested to ‘take the black’ Lord Arryn allowed it. After their house at large was found to also be at fault House Lynderly was ordered to pay 200gd to House Baelish and was stripped of two tracts of lands that were given to House Jasper. On recommendations from Ronnel and Teddy, Lord Arryn welcomed Petyr Baelish into his service as an advisor as he prepared to travel to the capital.

During the receiving of gifts after the wedding of Robert and Cersei Lord Arryn introduced Teddy and Ronnel Jasper who gifted a shadowcat to the royal couple. Jon Arryn met with Teddy and Jardon in the solar of the Tower of the Hand with Petyr Baelish in the days after the royal wedding. They requested his support in gaining entrance to the Red Keep’s library to find a map as they are sailing in search of treasure. Jon agreed and at Petyr’s suggestion imposed a 20% tax for the crown on the treasure.

Jon Arryn returned home to the Vale with his wife and Petyr Baelish in the Spring of 288AC for the first Spring Tourney in decades. He presided over the marquee event, the duel of Champions. When Ser Darron Brewlan won Lord Arryn spoke with him in the Gates of the Moon about his reward. Darron requested, and was gratned a royal pardon for all accused wrong doings from his past. Under questioning from Lord Arryn he denied one particular act, the theft of jewels from House Mullendore, in a most unconvincing way. Lord Arryn warned Darron that although his desired reward was granted that he would not provide any additional aid or support to House Jasper until the Mullendore property was returned.