They would replace long-serving directors Jim Scotland, Sam Robinson, and Danelle Dinsdale, and recently appointed Chris Tremain, Dan Druzianic, and Taine Randell. Council representatives were Mr Beaven and councillor Debbie Hewitt.
This comes as part of the discussion about HBRIC's future post-RWSS, and following a review of the council's capital and investments.
Mr Graham said they were recommending HBRIC have a limited mandate, and its board reduced to save costs while the company had a narrow focus.
"None of these new directors would receive extra payments for this role. The committee is also recommending that HBRIC administration be undertaken in house by the council's finance team.
"The council considers the current board of directors of HBRIC have served professionally and done what has been asked of them by the council, but it is now time to look to the future," he said.
HBRIC chairman Mr Tremain said the council recommendation came as no surprise.
Directors had recommended the board be reorganised, and its number of directors reduced after it became clear the council's appetite was not to expand HBRIC - with one of their suggestions that council directors replace the independent ones.
On how the board felt about the proposed change, he said: "My fellow directors and I are all professionals with Hawke's Bay's best interests in mind.
"To this end we will handle any transition in a professional manner."
When asked how he felt about concerns voiced, he said: "I am confident that councillors will make any such decision with a full understanding of the responsibilities of being a councillor together with the risks of being a director of an associated incorporated company."
Yesterday CE James Palmer said the council would also be recommended that for the immediate future, HBRIC should have a limited mandate.
A Statement of Intent is required for HBRIC for the coming year, requiring a clear mandate and budget approved by council.
"The council considers the current board of directors of HBRIC have served professionally and diligently, in service of council's set mandate. The committee also noted its thanks for their service to the region."
The council will consider this matter further at its meeting on March 28.