Judge Carmody is due to take over as leader of the state's court system next month.
He has firmly rejected claims he is politically biased for his perceived support of Newman Government policies.
But Mr Drummond said Judge Carmody's denials did not make much difference.
"It doesn't put this whole matter to rest for Judge Carmody to say... he'll be fiercely independent," he said.
"The point is if people have a justified perception he's biased, it's the same as if he's deeply biased."
Mr Drummond said Federal MP Clive Palmer's defamation battle with the Queensland Premier Campbell Newman, and possibly with Deputy Premier Jeff Seeney, could test the issue.
If other judges rule that Judge Carmody is disqualified from sitting on a case for apparent bias, what consequence does that have for his chief justiceship?Doug Drummond QC
"It's going to come before the court at some stage and it's not rocket science to start to wonder about whether if Judge Carmody sits on the case, there'll be a challenge by Palmer that he at least appears to be biased in favour of the other litigants," Mr Drummond said.
"It's not rocket science to foresee that's a possible situation."
Mr Drummond said if Judge Carmody's independence was questioned, the issue must be settled by other judges.
"Other judges will inevitably have to rule on that question - they may support him, but they may not - that provides an enormous problem," he said.
"If other judges rule that Judge Carmody is disqualified from sitting on a case for apparent bias, what consequence does that have for his chief justiceship?
"How can he continue to be Chief Justice."
Judge Carmody should have 'courage' to withdraw from position
Court of Appeal Justice John Muir also weighed into the debate last night, calling on Judge Carmody to withdraw from the position.
Justice Muir is the latest in a list of eminent legal figures questioning the elevation of Judge Carmody and the impartiality of the process.
In a speech to the North Queensland Bar Association, Justice Muir said it was the only appropriate course of action, given the unfortunate way the saga has unfolded and the obvious lack of support for the Chief Magistrate's elevation to the office.
No court, no matter how dedicated its members, can perform to anything like its full potential if the Chief Justice does not have the judges' respect and confidence.Justice John Muir
He also argued the controversy over the appointment has the potential to adversely affect the working of the Supreme Court and weaken public confidence in the administration of justice.
Justice Muir took a swipe at Judge Carmody's bid to sell himself to Queenslanders via media interviews, saying the public had been faced with the unseemly spectacle of a man soon-to-be Chief Justice spruiking his credentials.
"The qualities of competence, independence and impartiality in a Chief Justice are even more important than they are in a puisne (junior) judge," Justice Muir said in his speech.
"Their existence is established by conduct not assertion.
"A Chief Justice may influence and guide his judicial colleagues by the moral authority he exerts, the respect he commands and by his example, never by dictate."
'Not the smartest lawyer in the room'
Justice Muir said the insights provided were less than reassuring.
"He need not be the intellectual leader of the court, but he must command respect for his capability in discharging his judicial duties," Justice Muir said.
"He must certainly display no less intellectual rigour than the judges he leads.
"He will certainly have the respect and confidence of those he is to lead.
"No court, no matter how dedicated its members, can perform to anything like its full potential if the Chief Justice does not have the judges' respect and confidence."
Self-promotion calls independence into question
Justice Muir said the self-promotion also appeared to be meshed with the State Government's message over its decision to appoint him.
"The Chief Magistrate's self-promotion as a self-made man of humble background, accurate though it may be, meshed with the executive's message," he said.
"Ironically, the Chief Magistrate, when asserting his independence, was engaged in conduct that called it into question."
Justice Muir said Judge Carmody had no option but to withdraw from the role, due to the obvious lack of support from the legal fraternity and the unfortunate way in which the saga surrounding his appointment has unfolded.
"To take this course will require courage, but I do not apprehend that this is a quality that the Chief Magistrate lacks," he said.
Justice Muir is the 'first serving judge to speak out'
Civil libertarians say criticism of the appointment of the new Chief Justice of the Supreme Court is not coming from the usual quarters.
Australian Council for Civil Liberties president Terry O'Gorman has told Fairfax Radio that Justice Muir's comments are significant.
If you've got essentially a conga line of conservative lawyers saying this is a huge problem - then it follows - it is a huge problem.Terry O"Gorman from Qld Council for Civil Liberties
"If that's the case, then clearly Judge Carmody has a problem in going ahead and being sworn in."
Mr O'Gorman says many of the critics are seen as politically conservative, including retired judges Richard Chesterman and James Thomas, and former Queensland Bar Association president Peter Davis.
"If you've got essentially a conga line of conservative lawyers saying this is a huge problem - then it follows - it is a huge problem," he said.
Queensland Opposition Leader Annastacia Palaszczuk says it is unprecedented for a sitting judge to make scathing criticism of the new Chief Justice.
Ms Palaszczuk says Mr Bleijie must explain his decision and he should resign.
"We cannot have a situation where we have the Attorney-General of Queensland hiding in a corner like some little school kid, unprepared to face the music and explain his fundamental decision-making process," she said.
We cannot have a situation where we have the Attorney-General of Queensland hiding in a corner like some little school kid, unprepared to face the music and explain his fundamental decision-making process.Opposition Leader Annastacia Palaszczuk
A spokesman for Mr Bleijie says Judge Carmody has the keen legal knowledge, administrative skills and integrity that are essential qualities for the role of Chief Justice.
At a function on the Gold Coast, Queensland Treasurer Tim Nicholls tried to stay out of the controversy.
"I'm not prepared to weigh into that matter - that's something for the Premier and the Attorney-General - they've made statements on it," Mr Nicholls said.
"I'm looking at making sure that we can afford to provide law and order, that we can provide more police."
New Chief Magistrate announced
Meanwhile, the State Government has appointed a new Chief Magistrate to replace Judge Carmody.
Current Deputy Chief Magistrate Ray Rinaudo will be promoted to the role when Judge Carmody takes up his new position.
Mr Rinaudo has served as a Queensland Magistrate for nine years.
Leanne O'Shea will replace him as Deputy Chief Magistrate.
abc.net.au 20 Jun 2014
Every single person who sits in a place of business called a 'court' who is called a judge/magistrate/judicial clerk, etc is there UNLAWFULLY and therefore a criminal.
This is a fact that the corporate media does not report on.
Australia's judicature is a 100% corrupt organisation operating fraudulently.
The corporate media's silence on this matter is proof that they support this corporate fraud.