As your student has a diagnosis- make sure you have the diagnostic report – he can have the EAA needed as he has a medical diagnosis. An EP in no situation can be used for EAA.
However a medical diagnosis ( like ASD) means you must write a file note and ensure the arrangements he needs are established as his ‘normal way of working’.
As you have established this- make sure you can show evidence: for example teachers feed back saying he needs extra time and uses it. Also he may provide some feedback himself in a pupil view format, and you will also have evidence of him using it in previous mock exam sessions.
To confirm: you don’t not need to incur any further costs! You do not need another EP report, nor a medical letter (GP letters don’t count anyway).
Hope this helps,