Kristian Pulkownik, 33, is yet to formally apply for bail after he was arrested on Saturday following a march in Sydney's city centre where thousands defied coronavirus restrictions to attend.

He did not appear on screen for a second time this week at Sydney's Central Local Court on Thursday when his matter was mentioned.

The Surry Hills man allegedly struck a police horse and faces four charges for affray, animal cruelty, joining an unlawful assembly and failing to comply with a COVID-19 direction.

Barrister Hollie Blake in court said corrective services officers were continuing to make it impossible to gain access to the man.

Magistrate Mark Richardson read out a note from Parklea prison indicating that Pulkownik could not be brought up to an AVL suite to appear in court because he was "refusing to be tested".

"Your client is in custody and has been in the community and is at risk to others as he could be COVID-positive, and your client is in isolation," he said.

The judge suggested the lawyers make a Supreme Court application if they continued to take umbrage with the situation.

Outside court Pulkownik's lawyer Tony Nikolic said he had one quick five-minute phone call with his client where he indicated that he was "absolutely" interested in applying for release.

"But we can't take proper instructions and this is critical to the legal system ... we can't do much without proper full instructions," he said.

Mr Nikolic suggested prison guards could put a mobile phone in a plastic bag to allow for greater access to his client.

Pulkownik has spent five days in custody following the "Rally 4 Freedom" where a mass of unmasked protesters gathered in protest of state health orders.

Greater Sydney has been locked down for the past four weeks, with residents only able to leave home with a reasonable excuse.

The matter will return to court on August 11 when Pulkownik's lawyers said they would be making a bail application.

Australian Associated Press