Professional development goes by several names: continuing education, staff development, staff training, and in-service training (the last being the Library of Congress subject heading term).
Best practice for library staff from the IFLA Guidelines for Continuing Professional Development: Principles and Best Practices:
Best practice places responsibility for ongoing learning, based on regular assessment, on the individual practitioner. It demands actions to correct current performance gaps and to prepare for future responsibilities. There are several imperatives: one to support the employing organization’s goals for excellent service, another to further one’s own career development, and ultimately to contribute to profession-wide growth and improvement.