Final answer:
The sentence is mostly correct, but it combines tenses in a way that can be confusing. For clarity and correctness, it should be revised depending on whether the application to Tokyo University has already been made or not.
Step-by-step explanation:
The sentence "I have been intending to start learning Japanese even before I apply to Tokyo University" is mostly correct but could be improved for clarity. The phrase 'have been intending' correctly uses the present perfect continuous tense, which indicates an action that began in the past and is continuing into the present.
However, the use of 'even before I apply' suggests future intention, which could be confusing in combination with the present perfect continuous tense used earlier in the sentence.
To clarify the timeline and maintain the correct tense usage, consider revising the sentence to: "I had been intending to start learning Japanese even before I applied to Tokyo University" if you have already applied, or "I intend to start learning Japanese even before I apply to Tokyo University" if you have not yet applied.