The court reserved its decision on Wednesday after the Coalition government and the barrister representing Senator Gallagher, former solicitor-general Justin Gleeson, sparred over the limits of section 44 of the Constitution that bars dual citizens from sitting in Parliament.

A full bench of justices tested and queried arguments from Solicitor-General Stephen Donaghue and Mr Gleeson, and an adverse decision for Senator Gallagher could lead to a countback in Labor's ACT Senate seat finding her replacement.

Mr Donaghue told the High Court the Labor senator ignored the possibility her bid to renounce UK citizenship could have remained incomplete before the nomination deadline.

Mr Gleeson rejected the argument, referring to a submission the court received saying that overseas delays to applications renouncing citizenship could take up to years and - under the government's argument - require potential election candidates to act long before a poll was called without guarantee they could renounce, and then stand.

Documents provided to the Senate in December showed Senator Gallagher was "at the date of her nomination for the 2016 election, a British citizen by descent" and that her moves to renounce in April 2016 took until August 16 to be completed by UK officials.

Mr Donaghue said the time Senator Gallagher left before acting would have required UK officials to work four to five times faster than their average to meet the deadline for nomination. Mr Gleeson said this information wasn't available to candidates at the time of her application.

Senator Gallagher also overlooked information indicating she needed to provide the UK Home Office with evidence she was a British citizen when sending off her papers, and therefore failed to take reasonable steps needed to sever her citizenship ties with Britain, Mr Donaghue said.

Mr Gleeson denied this, saying Senator Gallagher had sent her Australian birth certificate establishing her father was born in Britain, and that a guide outlining documents needed to renounce citizenship did not indicate she must supply her parents' marriage certificate later requested by the UK government.

He told High Court justices that the senator took all steps required under UK law to relinquish her dual citizenship before the deadline for election candidates to nominate, and that she had declared her renunciation regardless of whether the British Home Office had processed it.

Unlike other parliamentarians referred to the court over dual citizenship, Senator Gallagher had renounced hers before nominations closed and elections writs were issued, Mr Gleeson said.

The actions of foreign officials and delays overseas in processing papers to renounce citizenship should not stop Australian citizens from participating in representative government, a principle that applied to all Australians who had renounced their dual nationality, he said.

Mr Donaghue said Senator Gallagher's arguments would mean that dual citizens could stand for and sit in Parliament.

UK laws did not pose an unreasonable barrier to Senator Gallagher giving up her citizenship, he said.

Senator Gallagher, the ACT's former chief minister, told the Senate in December she would stand aside from her responsibilities on Labor's frontbench until her case was resolved by the High Court, sitting as the Court of Disputed Returns.

Legal advice from British and Australian barristers says she took every reasonable step to renounce citizenship by descent from her English-born father Charles Gallagher before nominating, and that she meets the standard set by the High Court in recent section 44 cases.

Clarification: An earlier version of this story said the High Court was expected to decide on Senator Gallagher's eligibility on Thursday, March 15. The court reserved its decision and a date for the decision has not been set.