Is it necessary for calibration lab to carry out interlab comparisons or join a PT scheme?

It is a requirement of ISO 17025 and accreditation bodies for laboratories to monitor performance by comparison with results of other laboratories, where available and appropriate. If a formal PT or Interlab scheme is not available, then this is something you will discuss with your accreditation body and get their acceptance of your approach. Consider the intent – to ensure a laboratory does not have a bias in their results. As you are using a calibrated reference, this should be acceptable.

Thanks Tracey, that is good to know. The manufacturer of this reference device is ISO 9001-accredited but does not have ISO 17025 accreditation. Also they do not provide an uncertainty of measurement calculation for the device on the calibration certificate. We can run our own calibration on this device and calculate an uncertainty result. Is this acceptable considering we won't have a PT scheme or ILC ?

On the one hand that approach is the best you can do and it is anyway, all about assurance – that the result is valid. On the other hand, there are additional specific criteria that Calibration laboratories have to meet, established by the accreditation body. The reason, understandably, is that the calibration laboratory is issuing a certificate were the risk is that any errors will be  transferred to the testing laboratories. I suggest you discuss this with your accreditation body as it may be suitable and appropriate to seek accreditation as a testing laboratory where the lab effectively does quality control and verifies the performance of the produced equipment.