An employer is allowed to inform clients that a particular employee has left the company. This is particularly important where employees are assigned to clients and work closely with individual clients. It is good practice to inform clients of any material changes to the business, including with whom they will be dealing with.
However, an employer should generally not be disclosing anything more than the employee's name and when they will be parting ways with the company. Such statements should be neutral. They should not, for instance, be disclosing any reasons for leaving, any negative or defamatory statements associated with the employee, contact details of the employee etc.