Harrold Hardyng was the ward and squire of Anya Waynwood, Lady of Ironoaks Castle. He was later knighted by Bronze Yohn Royce. He is sometimes referred to as "Harry the Heir" though also referred to at the Young Falcon (similar to how Robert Stark was called the Young Wolf and Jaime Lannister the Young Lion in his youth) as he is the heir to young Lord Robert Arryn. Petyr Baelish hopes to make Harrold the Lord of the Eyrie and then marry him to Sansa Stark so that Winterfell may be claimed on her behalf.
Lord Jasper Arryn and his wife had three children: Jon, Alys, and Ronnel
Jon (who became Lord Jon on his father's death) married twice. Sadly both wives died. They had no children.
Alys (now deceased) married Ser Elys Waynwood (uncle of Lady Anya). They had eight girls and one son (named Jasper). Jasper and two of the girls died young. The eldest girl married Ser Denys Arryn.
Ser Ronnel married an unnamed girl from Belmore House. They had one son named Elbert. Ser Ronnel passed away.
Elbert was murdered by Mad King Aerys. Ser Denys died in the Battle of the Bells attempting to avenge his nephew. His wife died of grief and their newborn son died soon after.
Of the five remaining daughters of Alys and Ser Elys one became a Septa; one became a silent sister; one married the Lord of the Paps, but had no children; one was carried off by the Burning Men and never seen again; another married a landed knight sworn to the Waynwoods and had one son, Harrold, and then passed away. Harrold is thus the heir to the Lordship of the Eyrie should something happen to Lord Robert Arryn.
He has one illegitimate daughter he fathered on a serving girl named Cissy. Due to the weight she gained during her pregnancy, Harrold lost interest in her, and Lady Waynwood had her married to one of the castles men at arms. He is currently courting the daughter of a rich Gulltown merchant named Saffron. She is carrying Harolds second illegitimate child.