In 2366, Goddard was scheduled to rendezvous with the USS Enterprise-D, but the Enterprise was delayed by Starfleet to transport medical supplies to the Alpha Leonis system. (TNG: "The Vengeance Factor")
In 2368, the Goddard joined Captain Picard's fleet that blockaded the Klingon-Romulan border during the Klingon Civil War. The ship was one of twenty-three assembled for the fleet and was one of the seventeen chosen for the tachyon network. Identified by its name and registry number, the ship's position in the network was monitored from the Enterprise-D.
When the network was disrupted by a high-energy burst released by the Romulans, the net was no longer effective in a radius of ten million kilometers around the USS Sutherland. Subsequently, Picard ordered the fleet to proceed to Gamma Eridon at maximum warp, where the fleet would attempt to reestablish the net before the Romulans got there. (TNG: "Redemption II", okudagram)
In 2369, the Goddard was at Starbase 434 for resupply. The ship was named on the chart "Starfleet Operations-Sectors 21538-23079" in the Enterprise-D observation lounge. (TNG: "Chain of Command, Part I" okudagram)