Chair Mark Darrow said Davidson will hold the helm while the board looks for a permanent replacement.
“Gordon's leadership in the interim will ensure a smooth handover and provide consistency in leadership for the organisation through this time,” Darrow said in a statement.
Cooper will officially leave the bank at the end of September after five years of heading TSB but will be taking leave from July 28.
Cooper said she had steered TSB through a significant increase in regulation and growth in residential lending.
TSB's mortgage book grew by 42% to $6.2 billion between March 31, 2018 and March 31, 2023.
It's net profit in the latest year fell 47.6% to just below $20 million, largely because of a jump in personnel, IT and professional services costs.
Cooper said she felt the time was right to hand over to the next CEO while she spends more time off with her young whanau before looking for her next challenge.
“An incredibly busy five years has flown by quickly and I am proud of what TSB has achieved, as witnessed by the many customer and product awards gained by the bank in that period,” she said.
“I have been warmly welcomed by the Taranaki community and will always have fond memories of working with the Toi Foundation and TSB.”
Darrow said the board thanked Cooper “for her hard mahi over these last five years. TSB is such an important organisation for Taranaki, and indeed New Zealand, and we offer our thanks to her for leading the bank through a period of significant change.”