In general the first things you want to add to any program are the six main movement patterns:
1) Upper body vertical push/pull
2) Upper body horizontal push/pull
3) Lower body quad dominant/hip dominant
After that I generally make sure I'm covering the major joints:
Note: The Neck is a minor joint for this purpose.
Then if there is any room left I work the muscles that aren't already covered.
So in general, yeah I'd say that some form of upper body vertical push should be in your program.