As I write we are approaching an important date in the life of Project and Project Server 2013 – 10th April 2018 (thanks for the correction Andre!) will be the end of mainline support. This includes SharePoint Server 2013 too. This means that beyond this date we will only be taking fixes for the product that are security related (maybe recent regressions too). Hopefully you are already considering moving to Project Online, Project Server 2016 or possibly have an eye out for Project Server 2019. You need to be aware of other servicing policy details and this link is the place to go. https://technet.microsoft.com/en-us/library/mt493253.aspx
In brief – the most important paragraph is:
Starting with extended support on 4/11/2018, Microsoft will update the minimum supported build of SharePoint Server 2013 and SharePoint Foundation 2013. Customers must be running that build or higher to remain supported. If a customer contacts Microsoft support and their farm is not running the minimum supported build or higher, they will be asked to upgrade to that build before support can be offered.
The dates to be aware of:
SharePoint Server 2013 and SharePoint Foundation 2013 Releases Support End Date
Service Pack 1 4/10/2018
April 2017 Public Update – March 2018 Public Update 4/10/2019
April 2018 Public Update – all future Public Updates 4/11/2023
So by 4/11/2018 you should be running at least the April 2017 Public update, and hopefully something even more recent. For all updates for Project Server 2013 please see https://blogs.technet.microsoft.com/projectsupport/p/ps13cu/.