I have 2013 office license available in my organization. Am I entitled to use 2013 office license to use and will it be a problem from compliance perspective?

Discovery, Inventory and Compliance IT and Software Compliance
1

If you have software assurance ( maintenance) purchased, then you are entitled use next version of office product with same edition and you will be compliant provided 2010 and 2013 office deployment doesn’t exceed number of licenses procured.