Yes, but only if this is technically and, in your country, legally possible. At Berthold, we give our sources a recommended life-time of 15 years. After that we recommend to replace the source. Therefore, it is in the operator's responsibility to use the source longer.
Radiation detection technology has improved over the years. In radiometric systems that have been in operation for a long time, the activity of the radioactive source has decreased significantly due to natural decay. This causes less sensitive old detectors to be unable to reliably measure the respective process.
Since source replacement is costly, time consuming, and does not work towards a reduction in overall site source activity, in some cases it is advisable to replace the detector against a new and more sensitive detector and keep the source. Commonly, using a more sensitive detector, an additional 10 to 15 years of operation are possible with the existing measurement source left in place.