Tosefta for Horayot 19:7

Who is the nasi [that is obligated to bring an offering for sins committed before his appointment (Hor. 3:3, Hor. 10a:6)]? [He is] the "nasi" (per Vienna Man.) of Israel (i.e., the king), not the "nasi" of a tribe (i.e., a tribal leader, cf. Num. 7:2). [In the event that there is both] a "nasi of Israel" and a "nasi of the House of David" -- this one brings [a sacrifice of] his own, and that one brings [a sacrifice of] his own.