ISO 17025 accrediting

Yes, strictly speaking you can achieve accreditation in as much as you do not need to own the equipment. There are however some complications, especially if the other parties using the equipment are not accredited. 

It is necessary of course, to always meet the requirements in terms of suitability, calibration, maintenance and control to ensure the equipment is adequate and suitable for use when you use it. It would be no good if the other parties using the equipment, are not handling it appropriately. A formal arrangement of cooperation would be necessary. If the other parties are not accredited, then you would typically need to take care of calibrations and establishing management procedures and records that the other parties would also use. For example, filling in equipment events in the maintenance register, and cooperating when there are issues to investigate and correct, say in terms of equipment performance.

In terms of premises, your laboratory must be a legal entity and be accredited for a specific location and / or remote work.

For more information on ISO17025 requirements, see the articles

• What is ISO 17025 at https://advisera.com/17025academy/what-is-iso-17025/
• What does ISO 17025:2017 require for laboratory measurement equipment and related procedures? at https://advisera.com/17025academy/blog/2019/07/25/iso-17025-measurement-requirements-of-the-standard/

As long as you are able to meet ,sustain and maintain the requirements of ISO 17025 , accreditation can be achieved. But as you have mentioned having no equipments of own and using the rented ones, it would be very challenging to ensure that related requirements of ISO 17025 as rightly mentioned by Tracy evans. It will help greatly if other party which is renting the equipments have accreditation so that most of requirements gets covered at their end and other related ones at your end.

I am afraid that a broad answer only can given to your question.