TSB has been created by Lloyds Banking Group from a portfolio including Lloyds TSB Scotland.
It has 631 branches, including 189 in Scotland, but also seven operations and calls centres, including a 120-strong business banking team in Edinburgh.
Mr Pester has trumpeted TSB's local approach, with named branch managers, the provision of unused branch space to local businesses, and a local economy index to show where savers' deposits are being lent.
But he indicated there are limits to this localism.
"The branch manager cannot overrule central credit decisions," he said.
He added: "We believe centralised decision-making based on the amount of data we have across 4.6 million customers means we can extend more credit to more customers."
TSB's chief risk officer Neeta Atkar said: "We have to be responsible in our lending.
"The difference we will make is that we are committed to explaining much more to our customers on the occasions we say 'no'."
Bank of Scotland, another part of Lloyds, has also committed to putting more managers in its 294 branches.
TSB, due to be floated on the stock market in June, aims to be an "established challenger" but will focus on retaining customers when rules making bank switching easier come into force next week.