There are separate institutions for language learning situated in Singapore, which all have their own domains - but these domains can be difficult to find. For convenience's sake, we've compiled them here!
Alliance Française de Singapour is the French cultural hub of Singapore - they hold French movie screenings, workshops and more on top of their usual French courses which cater to people of different proficiencies and needs. They also host the DELF/DALF examinations in Singapore, which are internationally recognised French examinations. It's a great place to meet new people and practice if your target language is French!
The Japanese Cultural Society in Singapore boasts a myriad of Japanese cultural activities that you can take part in. They also offer language courses, and are the hosts for the JLPT (Japanese Language Proficiency Test) in Singapore. However, it is worth noting that the July test was cancelled and the December test is not accepting registrations! (2021)
Spanish World Group Singapore is part of an international group which promotes learning of the Spanish language, and are hosting the DELE examinations in Singapore. Likewise, they offer language courses for both children and adults - more precise information can be found on their page.
Singapore Korean International School, unlike the others mentioned above, do not offer Korean language courses as they are an international school. However, they are the hosts of the TOPIK exams (both I and II level) in Singapore. More information can be found on their page, though translations might be needed as the page is in Korean.
APICS offers Italian courses in both in-person and online formats, with a long and rich educational history in Singapore, experienced tutors and discounts when students purchase certain Italian products in Singapore. They handle the biennial CELI/CILS exam certification.
Goethe-Institut Singapore handles the German proficiency tests, TESTDAF and Zertifikats A1-C2. It also promotes German culture in Singapore and have been, along with their vast network of Goethe-Instituts, providing comprehensive language classes to interested individuals for seventy years.