Issues surrounding Bester's medical fitness could form part of the hearing, expected to begin on August 5 in Hobart Magistrates Court.
Bester, who pleaded not guilty in March 2023 to three counts of using a carriage service to menace, harass or cause offence, briefly appeared in court on Friday.
He is alleged to have made public posts on social media in relation to and directed at Ms Tame in April, July and August of 2022.
Bester was jailed in 2011 for abusing Grace Tame when she was a student at his school. (Bianca De Marchi/AAP PHOTOS)
Bester's lawyer Todd Kovacic said his client had been medically examined two weeks ago but he had only received the report on Thursday.
Mr Kovacic said he needed time to consider the report and flagged the potential of Bester changing his plea.
"The issue goes to fitness. I need time to consider that," he said.
Mr Kovacic described the not guilty plea as a "holding plea" and said "things may have changed" in light of the report, which he said needed to be provided to the Director of Public Prosecutions.
Magistrate Andrew McKee continued Bester's bail and relisted the matter for August 5 and 6, with the hearing expected to take at least a full day.
The case has been plagued by delays including previous adjournments to obtain medical reports.
Bester, a former teacher, was charged by police in October 2022 over the alleged online harassment.
He was convicted and sentenced in 2011 to two years and 10 months in jail for abusing Ms Tame when she was a student at his school and for possessing child exploitation material.
He served one year and nine months.
Ms Tame was the 2021 Australian of the Year and has advocated for abuse survivors.
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