The Office 2016 June 2017 updates and cumulative updates are now available, please see the links below:
Project 2016 June 2017 update:
The Office 2013 June 2017 updates and cumulative updates are now available, please see the links below:
Project Server 2013 June 2017 CU Server Roll up package:
Project Server 2013 June 2017 update:
Project 2013 June 2017 update:
Also worth noting, if you haven’t done so already, install Service Pack 1 http://support2.microsoft.com/kb/2880556 first if installing the June 2017 CU.
As always, fully test these updates on a replica test environment before deploying to production.