A draft data protection law has been under consideration by the Jordanian parliament for a number of years. It is unclear whether the draft law has been prepared with GDPR in mind, and the likely timeframe for it to become law is unclear.
There is no modern data protection law in Jordan, and there is accordingly no Data Protection Authority. There are Jordanian law considerations that could be material in the context of considering personal data processing activities, either in an HR context or more broadly. These range from general provisions protecting privacy or providing for remedies where someone causes damage to another. Depending on the circumstances of a data breach, it may be prudent to consider notifying law enforcement authorities and affected individuals, although there is no generally applicable legal obligation to do so.