Clancy called Flint on Monday to congratulate her on her election victory.
“I wish her well as she has been afforded the privilege to continue her role as your member for Boothby,” she told supporters on her Facebook page.
“I did so with the humbling knowledge that this was a tight contest.”
As voting continued, Flint was leading her Labor opponent 51.2 per cent to 48.8 per cent on a two-party basis.
With almost 80 per cent of ballots counted, the remaining pre-poll and postal votes were expected to favour the Liberal incumbent.
On the counting so far the swing to Labor was about 1.5 per cent, but less than the near three per cent the party needed to take the seat.
Clancy said Labor had run an “incredible campaign” with the party’s message heard loud and clear.
“Boothby deserves better hospitals, better schools and real action on climate change,” she said.
“I promise I will remain a fierce advocate for this community which raised me, shaped me and is home to my little family.”
Flint is yet to officially claim victory.
In Sydney, independent federal MP Kerryn Phelps has conceded defeat and congratulated the Liberal Party’s Dave Sharma for his win in the high-profile seat of Wentworth.
The race for the blue-ribbon seat had been neck and neck since Saturday night but Phelps conceded at midday on Monday.
“It’s been an enormous privilege to serve in Wentworth,” she told reporters while flanked by a group of her campaign volunteers.
“I wish Dave Sharma very well in his new role.”
Sharma at present has 51.7 per cent of the vote on a two-party preferred basis while Dr Phelps has 48.3 per cent with about 77 per cent of the ballots counted.
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