Simpson said she and Brown hadn't worked out what big policies in the mayor's programme they would agree on, including the council budget.
"I'm very aware of some of his key points he stood on. Auckland has voted for that and I think we need to respect that and we will have discussions on how they are debated and decided on around the governing body, around the Local Board table and in terms of CCOs (council-controlled organisations)," she said.
Asked if she would show the same loyalty to Brown as former deputy mayor Bill Cashmore showed to former Mayor Phil Goff, Simpson said she had huge admiration for Cashmore "but we are very different people".
"I will always have my own views and the mayor will be very clear about what they are. That's what a team does, they work together and nut things out, challenge each others' thinking on subjects and come to a decision," said Simpson.
Asked if he expected Simpson to support his major policies, Brown said he stood on four or five simple points and the overwhelming majority of people voted for him and all councillors.
"Going against those things will be going against votes that put them there in the first place," said Brown.
Simpson was widely tipped to become deputy mayor of the Super City.
As chair of the finance committee under Phil Goff, the three-term councillor won high praise for steering councillors through the Covid-impacted Emergency Budget containing a $900 million hole. She has also overseen tens of millions of dollars in savings as chair of the Value for Money committee.
The senior councillor and socialite is also the ideal person to undertake a lot of the ceremonial and civic functions that Brown is less keen on than his predecessors Phil Goff and Len Brown.
Brown said his first three weeks as mayor had been "interesting" and when pushed to elaborate said it had been "very interesting".
On the subject of a secret takeover of Ports of Auckland's operating business by the Dubai-based global port operator DP World, Brown said he had not quite got to the bottom of who at council was in talks.
"It doesn't really matter because it is not going to go anywhere," said Brown, who is opposed to the sale of a lease of the port business, or a sale of the land.
"I'm not running a detective story. It's not going to happen. We will move on to other things," he said.
Simpson said she was aware there had been an expression of interest from DP World to Auckland Council, but she couldn't recall when it was made.
Earlier in the day, Brown advised DP World and their bankers not to waste their investors' funds on proposals to take control of Auckland's waterfront port land, either by purchase or a long-term lease.
Auckland Council owns 100 per cent of the port company