Gardner's affair with Australian teammate Georgia Voll while married to ex-wife Monica Wright created headlines.
Wright publicly questioned the lack of action by CA in the wake of the affair, calling attention to "a clear power imbalance" when a senior member of staff has an affair with a junior.
Wright said Gardner should not be allowed to stay as vice-captain and questioned why CA had said nothing on the matter.
Cricket Australia CEO Todd Greenberg, speaking on SEN on Thursday, said "additional policies" would be put in place in situations where perceived or real conflicts of interest existed, when relationships between players had been disclosed.
He confirmed CA had been made aware of the relationship between Gardner and Voll before it appeared in the press, but also backed Gardner to stay in her position.
"Ash is a highly regarded leader in our system. The CA board make leadership decisions and have oversight over all leadership decisions," Greenberg said.
"Ash is our vice-captain for a reason, because she's highly regarded, but what we will do is in situations where there are personal relationships is make sure there are additional guardrails, so the perception of conflict or conflict itself - talking about things like selection - are handled appropriately and respectfully."
"We've got policies in place but we will put additional ones in place given Ash is now vice-captain. If there are relationships that have been disclosed and they have been, then we will make sure that conflict - perceived or real - around selections are removed, so Ash is not involved in those things."
Greenberg said the relationship between Gardner and Voll was "new news" in the media.
"But for those that were in the team and leading the team, we've been well across this for a period of time," he said.
Gardner addressed her affair and the position of the hierarchy in a post on Instagram.
"While my separation from my wife is a personal matter, I understand my current relationship status needed to be addressed by Cricket Australia given my position as vice-captain," Gardner wrote.
"I am grateful that the CA Board has chosen to support my continued leadership. I look forward to playing a strong role as a leader and providing the best possible support for my teammates in the season to come.
"I am grateful for the time Monica and I shared and sorry for the pain this has caused. I wish her nothing but happiness and success in the future.
"I won't be making any further public comment on this matter at this time and ask that the privacy of those involved is respected."
Greenberg made the point "respect" for all concerned was paramount.
"It is a very personal matter for the player, and I think there's a level of respect that needs to go with that," he said.
"Cricket's got very strong respect-at-work policies, so we've got a policy that's been developed over time that can deal with these sorts of things."
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