A good place to start: Musical America Worldwide provides current listings for a variety of opportunities

The Professional Growth tab takes you to 

• Job listings
• Contests & awards
• Educational opportunities, including scholarships and grants

•  Directory of Music Faculties in Colleges and Universities. Search for music degree programs (by type of degree, or by location)
• Graduate programs in musicology listed by the AMS
• Society of Composers provides guidance on choosing a grad school for composition

The Performing Arts Yearbook lists the most current information on competitions worldwide.  Includes descriptions, contact information, eligibility, and prizes.  2 volumes: 1. Europe; and 2. Asia, North America and the Pacific (aka, the “Rest of the World”)

These are print volumes, in the Music Library Reference Room. Call number: ML12 .M93 (2022-23)

Also, the print edition of Gramophone magazine (issued each January) lists competitions for the coming year.  Find it in the Music Library.

Along with Musical America Worldwide mentioned above, see also specific companies and organizations, such as:

Metropolitan Opera internships

SF Jazz internships

Spotify

Sirius XM

SONY Music

Atlantic Records

National Endowment for the Arts / Grants

Foundation Center

California Arts Council