You can certainly ask, but depending on what your terms of employment state, your company may not have to pay you for untaken holidays from previous years. Some companies have a "use them or lose them" policy. Companies are not required to carry over unused holidays from one holiday year to the next, but it can be arranged where the employer and the employee agree and the holiday leave is taken within the first 6 months of the following year.
Where I work, if you have untaken leave by the end of the holiday year, which is Jan-Dec, any untaken leave is paid with the last paycheck. We do not allow holidays to be carried over.
Having said all that, it is the employer's responsibility to ensure that every employee takes their full minimum annual leave entitlement each year, which is a minimum of 2 weeks after 8 months worked. If they do not, an employee can complain to the Rights Commissioner or the Labour Court.