Best was found guilty of telling jockey Paul John not to let two horses run as fast as possible.
But the BHA admitted to a "fairness" issue in its disciplinary process.
The authority used solicitor Matthew Lohn as chairman of its disciplinary panel when he was being paid by the regulator to advise on other matters.
A BHA spokesman said it takes "full responsibility" and apologised for "the fact that the non-disclosure of Mr Lohn's other paid work created an appearance of bias which led to the need for a rehearing".
"While there was no suggestion of any actual bias in this case, the BHA now accepts that it was an error not to disclose details of Mr Lohn's other paid work," the spokesman added.
Best has denied any wrongdoing.
Chief Executive Nick Rust said the authority would make a full statement once proceedings are concluded.
"While the BHA's disciplinary panels do not constitute judicial proceedings - we appoint members to disciplinary panels and we pay them to carry out their duties - our processes must not only be fair, but, particularly relevant in this case, be seen to be fair," he said.
Trainer Jim Best, who was given a four-year ban, will have his case reheard after the British Horseracing Authority issued an apology.