If your current leave to remain is the Tier 5 International Agreement Visa, you may be able to extend your leave under this visa category provided that you continue to meet the requirements of employment and current leave.
It is important to note that the maximum extension duration permissible under this route is 24 months. This however will not be the case if your initial application was made on or before the 5th of April 2012. Applications submitted after this date can only be extended for a maximum of 12 months at a time. The maximum period stay under this category is 6 years.
Also note that employees or civil servants in the household of diplomats who applied on or after the 6th of April 2012 can only extend their leave for a maximum period of 12 months at a time. The total period allowable in this instance is 5 years or the length of the employee's contract or posting or which ever is shorter.
Also note that you will be tied to your employer during the entire duration of your stay in the UK under this category. You will not be able to change employers.