Third party pressure arises when a customer or client threatens to withdraw their business unless you dismiss one of your employees. This may occur when the employer provides services to a client and employs people to work on behalf of the client, sometimes on their premises. Examples include security guards, cleaners, secretarial staff.
Because of this relationship your clients may from time to time request than an individual be removed from a job in accordance with their contract with you. In such circumstances you will need to investigate the reasons for such requests. There may be disciplinary action to take e.g. the security guard is on C.C.T.V asleep on duty. This would be normally viewed as gross misconduct warranting summary dismissal. You may take action short of dismissal such as a written warning for negligence in job performance E.G not adhering to cleaning frequencies.
If your client maintains their stance and you do not have grounds to terminate for conduct or capability issues, you will then need to take alternative steps to ensure that alternative work is provided. This would be on another contract with potentially different hours and on a different rate of pay.
If this is not possible the likely outcome will be termination with notice.