It’s common for instrumentalists to practice exercises and etudes to practice technique or expressive playing. These materials usually are never intended to be performed, but are instead done for the benefit they offer the musician. Composers can similarly practice composition exercises that aren’t intended to be heard by anyone, but help the composer get comfortable using a particular approach or get the creative juices flowing. Here’s a resource with 4 exercises.
Exercise 1: Compose Three Short One Minute Compositions
In this exercise you have two weeks to complete three short compositions. I like the idea of challenging yourself to complete something specific on a deadline. Some arranging commissions I have gotten are like this exercise, the client needs an arrangement of a specific tune by a specific date.
Exercise 1b: Compose One Composition Two Minutes Long
The details of this exercise include avoiding your compositional comfort zone. Again, it’s not an uncommon situation for a professional composer or arranger to be commissioned to write something that he or she might not take on as a personal project. It’s useful to be able to put your personal preferences aside and explore something completely different from your own style.
Exercise 2: Vocal Rhythms
Exercise 2b: Vocal Rhythms in a Foreign Language
I’ve used this idea many times. Select a text from somewhere and say it out loud rhythmically. Write out the rhythms you come up with and they can become the basis for an extended composition. As an aside, this works great with young music students to get them composing music together as a class. Ask them a question about what they did over the weekend and you might get an answer like, “Birthday parties, two in a row!”

Use these rhythms to create percussion music or add pitches to create a melody.
Check out the details of these exercises and then get composing.