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An alleged Sydney anti-lockdown protester accused of striking police horse Tobruk has been unable to speak with his lawyer, a court was told.

Kristian Pulkownik, 33, was arrested on Saturday evening following a "Rally 4 Freedom" march in Sydney's city where thousands defied coronavirus restrictions to attend.

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

"(The accused) did use unlawful violence towards NSW Police Horse Tobruk by conduct such that a person of reasonable firmness if present at the scene would have feared for their safety," court documents say.

The rally on Saturday moved from Sydney's Victoria Park to Town Hall where an unmasked crowd broke through a police barrier and continued down George St.

Lawyer Tony Nikolic said it was of great concern that he had been unable to speak with the accused while held in custody before his scheduled Sydney court appearance on Tuesday.

A court officer confirmed Pulkownik's case had been set down for the day but was "unavailable" for his appearance via AVL into the court.

"We've made a number of attempts with corrective (services), we knew he was at Surry Hills cells. What was most unfortunate they were giving us absolutely no information, actually hung up on us," Mr Nikolic told reporters outside court.

"We found that quite astounding given the gravity of the alleged offending.

"The fact that a lawyer can't get access to a client at the behest of his mother's request, his mother is worried sick - she has a heart condition ... that's not only a concern for justice in Australia but also human rights."

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

The lawyer sought orders allowing for immediate telephone contact with Pulkownik before his next appearance on Thursday where he is expected to apply for bail.

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Image Credit: Maksym Kozlenko, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons

The NSW government has begun the task of plotting Greater Sydney's COVID-19 settings for the coming months, with some restrictions potentially eased and others tightened.

NSW Health also believes it could vaccinate more than 350,000 people per week - if it had the requisite supply of the Pfizer jab.

With the city's lockdown scheduled to end on Friday, NSW recorded 145 new local COVID-19 cases in the 24 hours to 8pm on Sunday.

Of those, 51 were in the community for the entirety of their infectious period and 25 were in the community for part of their infectious period.

The NSW crisis cabinet met on Monday to devise a strategy to deal with the evolving crisis, and begin workshopping the restrictions to remain in place in Sydney over the coming months.

Premier Gladys Berejiklian said the government would this week settle on its post-July plans. Some restrictions may be tightened while others could be eased where transmission risk is minimal.

This may involve tightened or more targeted measures in virus-hit southwest and west Sydney, as well as changes to testing requirements.

However, some restrictions would remain until the majority of the NSW population was vaccinated, regardless of daily infection numbers.

The future of homeschooling is yet to be determined but construction activity, currently paused, will resume in some form from Saturday.

"We might need to go harder in some areas and release some settings in others," Ms Berejiklian told reporters.

"Our mission is to allow our citizens to live as safely and as freely as possible."

Chief Health Officer Kerry Chant said Greater Sydney's success rested on three factors - compliance with a tight lockdown, increased vaccination rates and the support and patience of the community.

She reiterated stronger lockdown measures would have marginal impact given the prevalence of transmission among critical workers who cannot stay home.

"The people of southwestern Sydney and western Sydney are the people that keep our city running. They do a lot of the work in distribution centres, food, logistics, transport," Dr Chant said.

"We should all reflect on that."

Dr Chant also indicated the NSW government would on Tuesday enable all people to walk up and receive the AstraZeneca vaccine at some locations.

She echoed updated expert immunisation advice that locked-down residents should "strongly consider" taking the AstraZeneca jab.

While Pfizer supplies remain constrained, the NSW government says it has plentiful AstraZeneca, which is effective in preventing hospitalisation or death.

Dr Chant also suggested NSW Health could administer more than 350,000 vaccines per week if its Pfizer supply was enhanced. This is separate from the federal government's vaccine rollout.

"We have to make really hard choices and what we're doing is looking at the best evidence (on) available supply," Dr Chant said.

"Ultimately, if we had more vaccine, we could do more ... but we do have a good vaccine, which is AstraZeneca."

It was later revealed frontline supermarket workers in five virus-affected western Sydney council areas would be eligible for priority Pfizer vaccination.

There are currently 44 COVID-19 patients in NSW in intensive care, of which 18 are ventilated.

Eight people have died during the latest outbreak, which began on June 16. This includes a Sydney-based Brazilian student in her 30s - the youngest woman to die of COVID-19 in Australia.

The fate of three local government areas in regional NSW areas due to exit a lockdown on July 28 is also unclear.

Frustration over lockdowns boiled over on Saturday when about 3000 people marched through Sydney's CBD in protest. Some 57 people have been charged to date.

Police Commissioner Mick Fuller said on Monday he was aware of online talk about another protest on Saturday, and emphasised any attendees would be arrested.

A full list of NSW exposure sites can be found at health.nsw.gov.au

© AAP 2021

Image Credit: Adam.J.W.C., CC BY 3.0 <https://creativecommons.org/licenses/by/3.0>, via Wikimedia Commons