After the downfall of Sauron, Gimli led a party of the Dwarves of Erebor to Aglarond, the Glittering Caves of the White Mountains within the realm of Rohan. There they founded a colony, and Gimli became known as the Lord of the Glittering Caves. His Dwarves performed great services for the Rohirrim and the Men of Gondor, of which the most famous was the making of new gates for Minas Tirith, forged out of mithril and steel.
We don't know exactly when Gimli established himself as Lord of the Glittering Caves, but it seems to be implied that it was not long after the Downfall of Sauron at the close of the Third Age. He would thus have been Lord for about one hundred and twenty years, until his departure from Middle-earth (or perhaps his death - sources leave room for doubt) in IV 120.
It is not established whether the title continued in use after this date. Gimli himself had no recorded heirs, but in principle another of his followers might have continued the Lordship in his place.
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