In employment law, dismissal as a result of personality clash can be a fair dismissal or a personality clash can occur that results in a dismissal for a different ‘permitted' reason, which can potentially lead to an unfair dismissal claim. If you think you have an issue with a personality clash between employees, you should take a very careful and well thought out approach to avoid an employment law claim.
It is good employment law practice to establish the root of the problem and you should always look an employee's record. For example, if you have an employee who has always had good appraisals and a new line manager is appointed who has problems with the performance or conduct of that employee, you should consider whether the new line manager simply wants to have their own hand picked staff. This is really a management issue as much as an employment law issue but one that requires very careful handling. If you allow the manager to go ahead with a disciplinary procedure, you may then find the employee raises a grievance and other issues come out of the woodwork. You may find discrimination or bullying is occurring.
This leads to the situation where personality may be the real reason for having to consider whether to dismiss an employee. If you have an employee who is negative or confrontational, or one who is a poor manager because they exercise overbearing supervision and bully or intimidate other employees, then you may be able to dismiss them as a consequence of their personality under the ‘some other substantial reason' ground. In order to do so, you need clear evidence of the problems that have been caused. For example, simply showing that their department is less productive and has a higher absence rate is insufficient. You would need to show that one, or preferably more, have taken time off for stress as a result of the employee's actions or have raised a grievance on such matters. It is important to follow a fair and transparent procedure and give the employee a warning about their behaviour and some opportunity to improve (although this may not always be necessary if you can show that the behaviour actually amounts to gross misconduct ).