A senior chief specialist was a specialist title held by Deep Space 9's Chief of Operations and Chief Engineer, Chief Petty Officer Miles O'Brien in 2370.
According to O'Brien, whenever he returned to Ireland, his father Michael O'Brien would introduce him as "my son, Senior Chief Specialist Miles Edward O'Brien." (DS9: "Shadowplay")
This obtuse and undefined term was used on a single occasion to describe an enlisted officer.
It was never alluded to if this was some sort of rank – such as some mashup of "Senior Chief [Petty Officer]" and "Specialist" becoming "Senior Chief Specialist" – or if it was associated with the fact that O'Brien held two positions aboard station.