Using the modern meaning of the word "Jewish" as someone who practices/practiced Judaism, There was not tribe that was Hebrew but not Jewish, because Jewish and Hebrew are basically the same ethnicity.

Note: Historically the word "Jew" originated as a description of the members of the tribe of Judah only. If you are a stickler for this meaning, then only the people of the Hebrew tribe of Judah were Jews, and the other 11 Hebrew tribes were Benjaminites, Reubenites, Gadites, etc.