Lieutenant Barnaby is the officer at the Enterprise-D's tactical station when Beverly Crusher commands a skeleton crew against a Borg ship in Descent, Part II.
Barnaby appears in Descent, Part II, the opening episode of the seventh season. With almost the entire crew on the surface searching for Data, Jean-Luc Picard leaves Dr. Crusher in command of the Enterprise with only a handful of officers, Barnaby among them.
When the Borg vessel returns, Crusher must pull out of orbit and then come back for the stranded teams. Barnaby mans tactical throughout, at first openly doubtful of the suggestions made by the inexperienced Ensign Taitt.
It is Taitt's idea, however, that saves them: the ship shelters inside a star behind an experimental metaphasic shield and triggers a solar eruption that destroys the Borg ship, with Barnaby carrying out the firing.