Starbase 621 was a Federation starbase administered by Starfleet.

The USS Enterprise-D was supposed to visit Starbase 621 in 2370, but delayed this mission for a few days to help in repairing the weather modification network of the Caldos colony. (TNG: "Sub Rosa")

Gul Dukat was being transported by the USS Honshu to Starbase 621 for the beginning of his war crimes hearing when the ship was destroyed and Dukat fled. (DS9: "Waltz")

This starbase was only mentioned in dialogue.
According to the Star Trek Encyclopedia (3rd ed., p. 466), after "The Neutral Zone" had aired, where Starbase 718 was mentioned in dialogue, it was decided that the starbase numbers shouldn't go much higher than 500.
According to Star Trek: Star Charts (p. 47) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), this starbase was located in the Alpha Quadrant.

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