If your supervisor or department head tells you that you can’t take a research leave now, what do you? Do you still apply or do you wait to apply?
You must apply for one simple reason. If you do not apply at your allocated time, you will lose this time toward the calculation of your next leave. First apply, have your proposal approved, and THEN negotiate the best time to take your leave. Keep a record of this any agreements in your files, just in case, it will be required later.
Remember, it is your right to take a research leave. It is the obligation of your library to enable you to do so. Your right to a research leave is the same as that given to any faculty at UT.