Solution:The National- School of Drama, Lalit Kala Academy, Sangeet Natak Academy, and Bhartendu Natya Academy are arranged in increasing order of their year of establishment. Sangeet Natak Academy was established first, followed by Lalit Kala Academy, then National School of Drama, and finally Bhartendu Natya Academy.
This order reflects the chronological foundation of these significant cultural institutions in India, highlighting their foundational roles in promoting various arts.