Karipa was appointed to the board in 2018.
His resignation meant the council had to approve a reduction in the minimum number of directors because the company’s constitution required no more than six and no fewer than three.
The change was approved unanimously at a meeting this week.
Kennedy said the outcome of an ongoing council CCO review was yet to be determined and the recruitment of a replacement director would likely “take a number of months”.
“Both existing directors - Declan Millan and Carolyn van Leuven are comfortable with the proposition.”
Councillor Philippa Baker-Hogan said she didn’t think it was ideal to have two directors overseeing a structure of the size of WDCHL but the remaining directors were capable and would have the support of a senior council officer.
Councillor Kate Joblin said she knew of companies bigger than WDCHL that had only one director.