The Curator Test controls access to the mission system and rewarded contributions, so Musixmatch keeps it open in a controlled way. Because of that, you may occasionally see the test marked as closed.
A closed test means the mission system for your language is currently full and not accepting new applicants.
The test reopens once your language's mission list has room for new contributors. The source material does not specify how far in advance a reopening is announced, or where to check reopening status for a specific language; no notification channel is stated.
While you wait, you can keep improving your skills and your knowledge of the writing guidelines by contributing on the website. That work also helps you pass the test and keep your Curator status once it reopens.