There’s no automatic entitlement but there’s nothing to stop you applying for a CID. You might ultimately have to slug it out at the WRC if there’s a difference of opinion.
CIDs can apply where contracts are extended to take the cumulative duration beyond the four year limit provided for in the legislation.
However, if there’s a clear distinction between the work you’ve been doing for the last 3.5 years and that which you would be doing for the next 16 months, the company could argue that the contracts are wholly different in nature and therefore not subject to the four year provision.