The USS Enterprise-C, being the fourth Federation starship named Enterprise was an Ambassador Class Starship commanded by Captain Rachel Garrett.
It was lost in 2344 after it answered a distress call from the Klingon's Narendra III outpost and engaged three attacking Romulan warbirds. This was felt by the Klingons to be a heroic sacrifice and it further advanced the growing trust between The Klingon Empire and the United Federation of Planets
See Yesterday's Enterprise (TNG)