The new cases came from more than 68,000 tests undertaken to 8pm on Tuesday and Premier Gladys Berejiklian said initial fears of a significant escalation in case numbers hadn't been realised.
Of the 22 cases, 11 were in isolation for the entirety of their infectious period. The tally for the outbreak that began on June 16 is now 171.
"Our fears about huge escalation haven't materialised and we certainly want to keep it that way," Ms Berejiklian told reporters on Wednesday.
Chief Health Officer Kerry Chant earlier told Sydney radio 2GB she expected a decline in case numbers around the end of the week, but only if people continue to adhere to lockdown rules.
"This really depends on how the community and businesses respond to our request to minimise those interactions," she said.
Agriculture Minister Adam Marshall is one of the people who contracted the virus at a Paddington pizzeria last week.
Mr Marshall is keen to get "any" available vaccine rather than wait for the Pfizer jab after Prime Minister Scott Morrison said under-40s can ask their GPs for the AstraZeneca jab instead.
The 35-year-old told Nine Network on Wednesday his illness had been "debilitating and quite eye-opening".
But Dr Chant stopped short of recommending younger people seek out AstraZeneca.
"Certainly, I'm very committed to following the (Australian Technical Advisory Group on Immunisation) advice," she said.
The prime minister's decision on Monday to allow under-40s access to AstraZeneca compares with official advice from ATAGI, which recommends AstraZeneca only be available to people over 60.
Dr Chant urged those who've had their first AstraZeneca shot to get their second.
She said younger people should discuss the matter with their GPs. But GPs may well prioritise the elderly, she said.
Meanwhile, NSW has tightened the rules for people travelling into the state if they have visited other regions.
NSW Health says people from areas in the Northern Territory, Queensland, and Western Australia now subject to stay-at-home rules should not travel to the state unless permitted to do so.
From Wednesday, anyone coming to NSW who has been in those areas in the previous 14 days must complete a declaration form.
Wednesday marks the fourth day of a lockdown for people in the Greater Sydney, Central Coast, Blue Mountains, Wollongong and Shellharbour regions.
The stay at home orders will be in place until at least July 9.
Ms Berejiklian has suggested the transmissibility of the Delta strain means some restrictions will likely remain in place, even after the current cluster is eradicated and the lockdown ends.
She said the state needs to get 80 per cent of its adult population vaccinated before it can adjust to "COVID-normal" life and open up.
The state is just over 20 per cent of the way to that goal.
