The third coast guard ship to bear the name, she was the flagship of the fleet and served in all three Cod Wars conflicts between Iceland and the United Kingdom.

The British destroyer Contest, which was on patrol in the area, fired three star shells, after which, Þór turned away and abandoned its attempts to arrest the trawler.

[6] On 11 December 1975, Þór, under the command of Helgi Hallvarðsson, was leaving port at Seyðisfjörður, where it had been minesweeping, when orders were received to investigate the presence of unidentified foreign vessels at the mouth of the fjord.

Another shot was fired from Þór as a result, this time a live round that hit the bow of Star Aquarius.

[10][11] In 1985, the ship was sold to the Icelandic Association for Search and Rescue and commissioned as Sæbjörg[12] where it served as a training vessel until 1998.