In the pay guidance released last week, the review was scheduled for mid-2023.
"We're in unusual and unpredictable times, and we've agreed to bring the review forward by a few months," Hipkins said.
"In good faith bargaining, there is room for compromise."
Speaking to the Herald, Wagstaff said this was a win for public sector workers.
"From our point of view, it worked," he said when asked about how the negotiations went.
"We asked for that [the guidance] to be reviewed with our input and our consolation and he [Hipkins] agreed," Wagstaff said.
"We said three years is a long time – we want to discuss it next year."
In Wagstaff's statement, he said there was an "absolute agreement" that bargaining will be in good faith without pre-determined outcomes.
"It was also agreed that there is scope to discuss cost of living increases in negotiations for all union members covered by collectives, with higher increases for low paid workers and that there is no pay freeze," he said.
Going forward, Wagstaff said the channels of communication are open – "we agreed to have further discussions,"
PSA National Secretary Kerry Davies said today's talks were "frank and constructive".
"There was agreement today that more workers should receive scheduled increases through step-based pay systems. Negotiations enable these pay systems to be implemented."
Hipkins was not available for comment after question time today, before speaking to reporters before Question Time he said that in "good faith bargaining there is room for compromise".
"We're trying to avoid getting into a cycle where the unions are incentivised to not settle – but we will look at it again next year."
In a further statement to media, Hipkins said the expectations set out last week "have not changed".
"We're in unusual and unpredictable times, and we've agreed to bring the review forward by a few months. It's worth taking stock at the end of 2022 to see whether the situation has changed sufficiently to revise the guidance," he said.
"We are committed to accelerating pay equity and parity processes and prioritising wellbeing and workload issues."