Sadly, there is no one agreed-upon definition of what constitutes a quality audit. The Center for Audit Quality (CAQ) identifies the following as the two primary pillars around which audit quality is built:
Auditor Expertise; and
Independence (*)
(*) Independence refers to external auditors’ interests being independent of those of company management
Several elements determine the quality of an audit; nevertheless, the combination of these two cornerstones increases the level of trust and confidence in business financial statements and serves as the foundation for the quality of an audit.
About the Center for Audit Quality (CAQ)
The Center for Audit Quality (CAQ) is an autonomous public policy organisation dedicated to enhancing investor confidence and public trust in the global capital markets. The CAQ fosters high-quality performance by public company auditors; convenes and collaborates with other stakeholders to advance the discussion of critical issues that require action and intervention; and advocates policies and standards that promote public company auditors’ objectivity, effectiveness, and responsiveness to dynamic market conditions. Based in Washington, DC, the CAQ is affiliated with the American Institute of CPAs. 
According to the International Auditing and Assurance Standards Board (IAASB), a quality audit is more likely to have been accomplished by an engagement team that:-
Exhibited appropriate values, ethics, and attitudes,
Was sufficiently knowledgeable, skilled, and experienced, and had sufficient time allocated to perform the audit work,
Applied a rigorous audit process and quality control procedures that complied with the law, regulation, and applicable standards,
Provided valuable and timely reports, and
Interacted appropriately with relevant stakeholders.
Audit Quality Standards
According to International Forum of Independent Audit Regulators (IFIAR), a robust quality control system is vital to enhancing and sustaining audit quality. As a result, quality control systems are a primary focus of many inspection Programmes.
A matter of particular concern is that inspectors' results about quality control inspections have fluctuated widely over time. Because of this, the International Accounting Standards Board (IAASB) issued two new standards in December 2020 to reinforce and modernise how firms use quality management:-
ISQM 1 Quality Management for Firms that Perform Audits or Reviews of Financial Statements, or Other Assurance or Related Services Engagements
ISQM 2 Engagement Quality Reviews
These standards direct audit firms to improve the robustness of their monitoring and remediation, embed quality into their corporate culture and the "tone at the top," and improve the robustness of engagement quality reviews.
In June of 2022, the Auditing Standards Board (ASB, which is the AICPA's senior committee for auditing, attestation, and quality control applicable to the performance and issuance of audit and attestation reports for non-issuers.) adopted comparable standards.
In Malaysia
These two new Quality Management Standards have also been approved by the Malaysian Institute of Accountants on 17 September 2021
These standards will come into effect on 15 December 2022, in line with all major jurisdictions adopting the ISQM and ISAs.