The broadcaster has joined Swiss clinic Dignitas, which lets people have an assisted death, but her family could currently be prosecuted if they were to travel there with her.
Dame Esther told the BBC it was “important that the law catches up with what the country wants”.
Assisted dying is banned in England, Wales and Northern Ireland, with those convicted facing up to 14 years in jail.
In Scotland, it is not a specific criminal offence, but assisting the death of someone can leave a person open to murder or other charges.
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What is assisted dying?
Starmer: Free vote ‘seems appropriate’
Sir Keir voted in favour of legislating for assisted dying in 2015, when a private members bill was brought to the Commons by Labour MP Rob Marris.
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Members were given a free vote on the issue – meaning their political parties did not pressure them to vote in a particular way – and they overwhelmingly rejected a change in the law by 330 votes to 118.
Sir Keir said while there are “obviously strong views both ways on this, which I respect”, another private member’s bill and free vote “seems appropriate”.
Both Housing Secretary Michael Gove and Work and Pensions Secretary Mel Stride have also said they would be willing to see a fresh parliamentary debate on the issue.
The prime minister’s official spokesman said the government’s position has not changed, so it remains a matter for parliament to decide and “an issue of conscience for individual parliamentarians rather than government policy”.