Here is a typical formal business letter for this...
Dear Sirs:
I took the IELTS test in May and would like to retake the test in the future. How soon can I do so?
Thanks for you help.
Sincerely,
Jane Doe
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Some comments:
No need to use "Dear Sir or Madam' just use 'Sirs'. In this context, both genders are implied.
I would not use "To whom it may concern" since you know whom it concerns, i.e., the administrators of the test.
If you are writing this as an email, the "Dear Sirs" is optional. You can simply start with the first paragraph.
You don't need to use impersonal style, i.e., 'how can one do it?'. That style is not common in normal business letters and would sound too formal. Just say 'how can I do it?'
In my view the "Thanks in advance" or "thanks for your help" is optional. Saying thanks is common, but in reality is a bit of fluff that is not really needed in a business letter. You could leave out that sentence and have a tighter letter. You would not offend the recipient.