A man has been accused of attempting to extort a woman over her alleged relationship with a well-known Queensland public figure.

The three parties involved have had their identities suppressed with a gag order after the accused male appeared on Friday in Cairns Magistrates' Court on an extortion with domestic violence charge.

It's alleged the accused had attempted to extort the woman over what he claimed was a relationship with a high-profile man.

The suspect had previously been granted bail.

Defence barrister Brydie Bilic told the court the 'authenticity of the evidence of the relationship was not challenged'.

She said her client's original bail terms, put in place before Friday's hearing, were 'overarching', reported the ABC.

'There are concerns that it is designed to protect,' Ms Bilic told the court.

'There are some matters that go so far as to potentially constitute a gag order.'

Ms Bilic requested the non-publication order not include the high-profile person and added that he was not a witness in the case.

She told the court that the alleged victim and the high-profile figure don't live together or even in the same area.

She said she believed there was no evidence of easily available information that would link the two.

'His [the high-profile man] name arises in the factual context of the allegations, but that doesn't make him a party to the proceedings.'

Magistrate Meoli, however, ordered the names of the accused, the woman and the high-profile person all be suppressed.

The suspect's bail was extended with the matter adjourned to a later date.