The King of Tripura, whom Rabindranath Tagore met for the first time, was

A "first meeting" question about a princely-state patron hinges on a distinction between a literary CORRESPONDENCE and an actual, in-person MEETING. A first face-to-face meeting between two people can happen anywhere they both happen to be present together -- a shared city, a hill station -- not necessarily in the patron's own home state, so the date of the first LETTER and the date of the first VISIT TO THE STATE ITSELF can each be mistaken for the date of the first personal encounter.

1. 1882: Maharaja Bir Chandra Manikya (reign 1862-1896), grieving his queen consort's death, was deeply moved by the young poet's verse "Bhagna Hridaya" and sent his emissary Radharaman Ghosh to Tagore's Jorasanko home in Calcutta to convey his admiration -- correspondence through a proxy, not a meeting.

2. 1886: Tagore wrote his first direct letter to Bir Chandra Manikya -- still only correspondence.

3. By around 1890, having already progressed beyond letters, Bir Chandra Manikya began inviting Tagore to his camp on every visit to Calcutta, and the two spent evenings discussing poetry and music -- their first face-to-face meetings, since every contact between them before this point had been through a proxy (1882) or by letter (1886).

4. 1894: Bir Chandra Manikya travelled to Kurseong for a change of air and took Tagore along with him; they talked late into the night on literature, art and photography.

5. October 1896: Tagore was again the Maharaja's guest at Kurseong, only weeks before Bir Chandra Manikya's death in Calcutta on 11 December 1896.

6. 12 December 1896: Radha Kishore Manikya succeeded his father as Maharaja of Tripura.

Radha Kishore Manikya's friendship with Tagore only deepened in the years after he became king, and Tagore's own first visit to Tripura itself -- its capital Agartala -- did not happen until early 1900, at Radha Kishore's invitation. That 1900 visit is Tagore's first visit to the STATE, a distinct fact that this question's wording invites confusion with. Since Tagore had already met Radha Kishore's father, Bir Chandra Manikya, face to face repeatedly through the early-to-mid 1890s in Calcutta and at Kurseong -- years before Radha Kishore even took the throne -- the King of Tripura whom Tagore met for the first time was Maharaja Bir Chandra Manikya.

This sequence is documented in the Government of Tripura's own published record of the relationship, "Tagore and Four Princes of Tripura" (Tribal Research and Cultural Institute, Government of Tripura), whose chronology places Tagore's Calcutta and Kurseong meetings with Bir Chandra Manikya in the early-to-mid 1890s and his first visit to Agartala only in 1900 under Radha Kishore Manikya.