A Rajarshi is a king who turned into a royal sage, or Rajarshi. A rajarshi will not have to leave the kingship to became rishi as in the example of Vishwamitra (who later advanced to becoming a Brahmarishi) but still while ruling the kingdom has reached a state of rishi and have attained self-realization.
"Rajarshi" is the name of the novel by Rabindranath Tagore, based on the life of a king of the state of Tripura, named Govindamanikya. Purushottam Das Tandon, freedom fighter from India was addressed reverentially as "Rajarshi." Chatrapati Shahu, ruler of princely state of Kolhapur, well known for his social reforms in modern India is remembered as Rajarshi. Rajarshi Udai Pratap (Bhinga Raj). Mr. James Jesse Lynn, disciple of Paramhansa Yogananda was also referred to by the title of the Rajarshi, as Rajarsi Janakananda.