Is it mandatory to write a specific procedure for impartiality?

There is no mandatory requirement to have a procedure or documented procedure regarding impartiality. Typically you will ensure safeguarding impartiality through stating your commitment and approach in a Quality Policy as well as the Quality Manual (if you have one).

Other processes that include considering and evaluating risks to impartiality are Internal Audits, Addressing Risk and Opportunities, and Management Review. Risk assessments must be used to demonstrate the ongoing attention and identification of impartiality risks.

Have a look at the Article  How to ensure impartiality in an ISO 17025 laboratory at https://advisera.com/17025academy/blog/2020/10/12/ensuring-impartiality-in-an-iso-17025-laboratory/ for Five steps to ensure impartiality.