I think his sole claim to fame was his long lifespan, which was surpassed in Middle-earth only by Bilbo.
As far as I can tell, Tolkien never wrote any stories specifically about Gerontius Took. We do know that he was the twenty-sixth Thain of the Shire (from T.A. 2848 to T.A. 2920); he was married to Adamanta Chubb; they had twelve children; one of his sons (Hildifons) left the Shire on a journey and never returned; another son went on an adventure in his youth to see the Sea; his three youngest daughters (Belladonna, Donnamira and Mirabella) were known as the three remarkable Took sisters; and, of course, the Old Took lived to the age of 130 which no other Hobbit surpassed before Bilbo Baggins.