Here are two older examples. The first is ancient Mouseion (Musaeum) founded c. 300 BC after the Alexandrian conquests that briefly unified the Hellenistic world, a prototype of modern academies. However it had broad scope not restricted to a specific research project. Its classical age ended with the expulsion of intellectuals from Alexandria in 145 BC by Ptolemy VIII:
"The Musaeum was an institution founded, according to Johannes Tzetzes, by Ptolemy I Soter (c. 367 BC – c. 283 BC) at Alexandria... Rather than simply a museum in the sense that has developed since the Renaissance, it was an institution that brought together some of the best scholars of the Hellenistic world, as Germain Bazin compared it, "analogous to the modern Institute for Advanced Study in Princeton or to the Collège de France in Paris."... More than 1,000 scholars lived in the Mouseion at a given time. Staff members and scholars were salaried by the Mouseion and paid no taxes."
The second is
Maragheh observatory founded by al-Tusi in 1259, who justified the undertaking to Hulagu, Genghis Khan's grandchild, by the need to compile new astronomical tables adapted to Persian locations:
"Men of mathematics, science, and astronomy came to the Maragheh Observatory from across the Islamic world and further. According to historical texts recovered from the observatory, the site had a reputation so widespread it had reached as far as China... A number of other prominent astronomers worked with Tusi at the observatory, such as Muhyi al-Din al-Maghribi, Mu'ayyid al-Din al-'Urdi, from Damascus, Qutb al-Din al-Shirazi, and Hulagu's Chinese astronomer Fao Munji, whose Chinese astronomical experience brought improvements to the Ptolemaic system used by Tusi. After 12 years of intense work by Tusi and other scientists... the tables were compiled in the Zij-i Ilkhani."
The obsevatory lost its funding after 1282, and became inactive by c. 1300.