The Gemara in מסכת תענית speaks about the special role of certain individuals in Jewish life. It mentions the king, the Kohein Gadol, and the regular Kohein.
Because of their special tasks, it was important that they looked respectful.
The king had to get a haircut every day. The Kohein Gadol, every Thursday in time for the changing of the guard each Shabbat. The regular Kohein had to get a haircut once a month.
This was learned from the Nazir, who usually took on the Nazir period for thirty days when he would cut his hair.
The Gemara goes on to say that Kohanim need to be on call nowadays for the rebuilding of the third Temple. Therefore, they should keep their hair short and they should refrain from drinking wine. The Temple could appear at any time, and the Kohanim need to be ready to jump in and do their priestly duties. May it come speedily.