Becoming expert in quality of pathology lab

To answer your question, lets distinguish between management and technical quality. While quality assurance approaches are similar in all laboratories, pathology has a diagnostic aspect not typically addressed by testing and calibration laboratories. Although veterinary accreditation programs are covered by ISO 17025, the International standard applicable to medical pathology is ISO 15189:2012 Medical laboratories — Requirements for quality and competence. When looking at management quality activities such as document control, auditing and improvement, both ISO 17025 and 15189 follow the same approach, in accordance to ISO 9001.

Understanding the purpose of the tests (what the results are being used for) and associated risks is crucial to developing skill as an expert. If you are referring to technical quality, I would suggest you obtain training on topics such as risks (as relate to diagnostic methods), method validation, internal and external quality control. Find opportunity to develop your skills in internal auditing and addressing nonconformances, root cause analysis an corrective action.

Generally, a knowledge of ISO 9001 will be an advantage, as ISO 15189 incorporates ISO 9001 principles, like ISO 17025, into the standard. Have a look at the ISO 9001:2015 Foundations Course at https://advisera.com/training/iso-9001-foundations-course/
Also look at the available information in the ISO 17005 and 9001 learning centres, available at the Advisera academies at https://advisera.com/17025academy/ and https://advisera.com/9001academy/