A conscience vote, or free vote, means that members of parliament are not obliged to vote with their party; instead, they can vote according to their own beliefs. Each parliamentary party decides if its members are allowed a conscience vote on a particular issue.
The Governor-General is the Queen’s representative in Australia. They have some of the responsibility for ensuring that Australia is governed according to the Constitution. Although the Governor-General, on behalf of the Queen, has a role in both the government and the Parliament, they are not an elected member of parliament. As a result, they are not involved in the process of a conscience vote in Parliament.