"We have seen some of those communities go from rates of around 19 or 20 per cent up to nearly 90 per cent and that is extremely encouraging."
Fully vaccinated adults in the 12 government areas will from Monday be able to exercise outdoors with no time limits, and gather in groups of five for outdoor recreation within five kilometres from home.
Children under 12 are not included in the gathering limit.
From Monday 27 September, all public pools across NSW will be able to open with a COVID-safe plan in place.
"All of us appreciate the importance of enjoying the warmer weather - and the positive mental health benefits from recreation and exercise," Ms Berejiklian said on Sunday.
Conditions for authorised workers and travel permit requirements will remain in place in the LGAs of concern, however.
Cumberland City Council Mayor Steve Christou welcomed the changes, saying it is important there is "equality across the city" with how restrictions are applied.
"The reopening of swimming pools will make a big difference to our community who have been locked down for months under the strict conditions," he said on Sunday.
"Having an extra recreational and exercise activity will make a huge difference to the mental health of residents, particularly children who are now on holidays after a term of home schooling."
Monday is also the deadline for authorised workers to have been inoculated with at least one COVID-19 vaccine dose to be permitted to leave their LGA for work, unless they have a medical exemption.
NSW reports 1,083 new COVID-19 cases
Despite the relaxation of some restrictions, the premier warned the state's situation remains "precarious", as NSW reported 13 deaths on Sunday - an outbreak record.
"We are anticipating our worst weeks in ICU and hospitals will be in October," she said.
Of the 13 people who died with COVID-19 in the latest reporting period, one was in their 40s, two in their 50s, two in their 60s, five in their 70s, and three in their 80s.
There are 1,238 COVID-19 cases in hospital, with 234 people in intensive care, 123 of whom require ventilation.
NSW Health's Dr Jeremy McAnulty said while he was pleased to see the number of new infections fall on Sunday, that did not necessarily mean the peak had passed.
"We don't want to jump the gun. We do like to see several days before we can call it a trend, but certainly cases overall have been going up. They have stabilised and appear to be dropping in some areas," he said.
"We need to keep our guard up, and we have got a way to go before we can be reassured that numbers are on the way down."
Across the state, 81.9 per cent of people over the age of 16 have had one dose of a vaccine, and 51.9 per cent are fully vaccinated.
The premier said 17 per cent of the state's 12 to 15-year-olds have also had their first dose.
With SBS News