Can a patent practitioner not of record conduct an interview?

Yes, a registered patent practitioner who is not of record can conduct an interview if they have proper authorization from the applicant. According to MPEP 405:

Interviews may be conducted with a registered practitioner who has proper authority from the applicant, or an attorney or agent of record in the form of a power of attorney or authorization to act in a representative capacity, whether or not the practitioner has a copy of the application file.

The practitioner can show authorization by completing, signing, and filing an Applicant Initiated Interview Request Form (PTOL-413A) or using Form/PTO/SB/84, ‘Authorization to Act in a Representative Capacity’.