Let me answer your question not as an internal in-house license but an official IATA Dangerous Goods Diploma. First, please check the validity date on the 2011 DG Diploma. Please confirm that it says: “Valid until 31 December 2013”. Then, please check the 2013 Diploma and ascertain whether it says: “Valid until 31 December 2015”.
If so, you can take a Recurrent test on or before 31 December 2015 and get your certificate extended for another two years. As prerequisite, I take that your license covers “Category 6 including Radioactive Material”, you need to take a recurrent course covering “Category 6 including Radioactive Material”.
For instance, a Category 3 license holder cannot take a Category 6 recurrent course. It is mandatory for airline employees to hold a “Category 6 including Radioactive Material” license since a Category 3 license is not sufficient. For IATA licenses, as long as you qualify the once in 2 years recurrent course, your validation date will always be 31 December.
You can attend the recurrent course 3 months in advance, i.e., since your validation date is 31 December, you can take a recurrent course during the period from October 1 to December 31. Should you take a recurrent course in September, you lose this privilege. For in-house licenses, please ask your company.