I agree with TallPaul - that description of what will occur following to your 'representation' to the TD is fairly accurate.
I note you don't mention what exactly the 'issue' is you have with the Department. If it is a case for example that you have been refused a payment or something, there are often appeals mechanisms in place - have you considered this option or have you already exhausted this avenue?
On the other hand, if your difficulty concerns a customer service-related matter and a government department, there are dedicated Customer Service Managers in each Department who are responsible for dealing with complaints.
I am familiar with some of these appeals mechanisms, where to complain, the various Departments, etc. so if I can be of any further help, you might PM me.
CMCR