The regional NSW seat of Farrer will open up after Sussan Ley's formal resignation, which is expected to be a hotly contested four-way battle.
Ms Ley outlined a list of her proudest achievements and delivered a parting shot at Mr Taylor who became the Liberal leader in an emphatic party room victory earlier in February.
"It will be for commentators and historians to measure the period of my leadership," she said in a statement on Friday.
"I welcome the coalition's immediate re-adoption of many of these directions and policies in recent days and weeks."
Ms Ley, who held her seat for 25 years, said it was crucial the Liberals maintained Farrer as the coalition has held it since its creation in 1949.
"I know that Angus Taylor can and will ensure the party continues to enjoy the support, trust and confidence of the people of Farrer," she said.
Among coalition ranks, the vote is viewed as the first major test of Mr Taylor's leadership.
Fellow independents David Pocock and Helen Haines publicly endorsed Michelle Milthorpe on Friday, kicking off the campaign for Farrer, even though a by-election date is yet to be set.
Mrs Milthorpe ran against Ms Ley in the 2025 federal election, losing 56.2 to 43.8 per cent after preferences, narrowing Ms Ley's margin to 6.2 per cent.
"We are not a safe seat anymore and this is our time to make change," Mrs Milthorpe told reporters in Albury.
Advocating for a fit-for-purpose hospital, farmers and calling for a Royal Commission into water after years of mismanagement are some of the first items on her agenda, she said.
Mr Taylor said Ms Ley made a massive contribution to the Liberals and the nation, admitting the by-election would be hard to win.
"The Farrer by-election is going to be very, very tough," he told reporters in Sydney.
The Liberals, Nationals and One Nation are all expected to run candidates, but are yet to announce them for the upcoming vote.
"We have seen parties who are too busy fighting one another to represent us, so they're looking elsewhere (to One Nation)," Mrs Milthorpe said.
"I do challenge people to look at independent representation."
After being deposed as opposition leader, Ms Ley said she would spend the following weeks thanking her constituents before tendering her resignation.
But one senior Liberal source said Ms Ley had not been heard from since the spill and had not reached out to any of the local party membership.
Ms Ley's office did not respond to a request for comment.
State Liberal MP for Albury Justin Clancy ruled himself out of the race on Friday morning, citing family commitments.
Party insiders feared losing Farrer and the state seat of Albury if Mr Clancy wasn't successful in the by-election.
One Nation plans to reveal its final three or four nominations next week, with a pre-selection event scheduled for March 7 to choose its official candidate.