You do not mention whether the three directors have shares in the company and in what proportions. You also do not mention what each director contributes to the business in terms of their duties. Nor what each brought into the business at its commencement. Finally there is no information on how the company has traded since incorporation. Because of the lack of all this specific information any answer can only be in the most general of terms. You need to seek professional advice of a solicitor or an accountant.
Basically the two directors who ‘get on’ have to decide whether to try to get rid of the third by either sacking him or trying to offer him an incentive to leave. There could be employment law issues, protection of minority shareholder issues and practical issues to overcome. On this last front you have to ask yourselves:
• What the third director has brought to the company. Is it know-how, contacts, customers or assets/ money?
• What agreements did you enter into when you started the company?
• How would you fare if he were to leave?
• Finally how much would it cost in legal fees and in compensation for him to leave or for you to remove him?
You might decide that the easiest and least costly way out might be for the two of you to leave and set up in competition.
If the director is not a shareholder the shareholders can meet and pass a resolution terminating his employment. If he is a shareholder it will depend upon what percentage of the shares he owns. In addition you would be expected to honour the termination clauses in any contract of employment. If he does not have a written contract of employment, as the company has been trading less than a year you can terminate his employment without the director having recourse to unfair dismissal legislation.
If the director has a shareholding there are laws to prevent him from being persecuted.