In general, the elder son of a king will become the next king, if eligible.
In which occupations the brothers of the next king (elder brother) will settle? Does it depends on individual or will there be any occupation for them?
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Here are two verses showing about brother's activities.
SB 9.11.25: Śukadeva Gosvāmī replied: After accepting the throne of the government by the fervent request of His younger brother Bharata, Lord Rāmacandra ordered His younger brothers to go out and conquer the entire world, while He personally remained in the capital to give audience to all the citizens and residents of the palace and supervise the governmental affairs with His other assistants.
SB 5.5.20: My dear boys, you are all born of My heart, which is the seat of all spiritual qualities. Therefore you should not be like materialistic and envious men. You should accept your eldest brother, Bharata, who is exalted in devotional service. If you engage yourselves in Bharata’s service, your service to him will include My service, and you will rule the citizens automatically.
We may conclude that other brothers assist the elder brother's activities as the king.
A brief answer can be found in a book named "Studies in Hindu Law and Dharmaśāstra" written by Ludo Rocher . Page 337.
The author is quoting Shukra Niti Sara (शुक्रनिती सार) . And is clearly mentioning the occupations of brothers of a king.
The text adds that younger brothers should rather be appointed governors of the provinces or superintendents of the royal stables , the treasury etc. ( Shukra Niti Sara 1.346-48)
So it's clear that the kings brothers should be appointed on very high and respectable as well as very important positions as his aid.