You need to check out the fixed term contracts rules with D/ET&E.
If your contract has a specific term i.e. 3 year & 14 day, and is a temporary contract, then they can let you go at the end of this contract.
If you have had a number of back to back contracts, then, in certain circumstances, you automatically become permanent - this is national employment law that applies in all jobs, not public service rules.
One thing to bear in mind about the public service, is that you cannot get an established permanent job in civil service unless you have been successful in a competition for a permanent job or a post that will become permanent after a certain period of time. This often leads to exisiting contract job holders having to compete for their own jobs if the post is made permanent.