Kaylene Holland, one of Clutha Community Health Company Ltd’s (CCHCL) directors, has left.
CCHCL trades as Clutha Health First and the directors are responsible for its overall governance.
CCHCL chairman Brian Dodds said the board typically had either six or seven members.
It had managed to operate "for some time" with only five members after Ms Holland’s departure.
However, the board now sought two new directors to bring the number back up to a more manageable seven.
Mr Dodds said five was "a bit on the light side".
"It’s just a case of opportunity to try and rebalance."
Nominations for the two director positions had opened and were due to close next Friday.
Mr Dodds wanted more balance on the board in terms of representation locally and from outside the area.
He also said it was important to ensure a continuing succession of directors.
Mr Dodds had previously indicated he intended to retire from CCHCL sometime.
A third of the board typically came up for re-election within the organisation but the two directors being sought was not a part of that process, Mr Dodds said.
Clutha Health First trustees would receive the nominations and make a shortlist before making a decision.
Mr Dodds anticipated the new directors would be appointed by the end of August and begin their term in September.
