Donald Trump is a former Democrat, and has never served in Washington D.C. before, so there is a whole set of political connections that he is disconnected from that career politicians normally have going into office. Will the Republican party step up to help Trump in this regard by getting solid members ready for a Cabinet? I hope so.
The military will continue to shrink under Trump, the Republican majority in the House and Senate are stuck with Sequestration and that’s that. The rate of shrink might slow down a little bit as the world isn’t exactly a safer place than it was in August of 2001 when the US Army stood firm at 490,000 and ten active divisions worth of combat power. Sequestration has the Army shrinking very quickly below that level of capability.
I expect that relations with both Russia and China will improve. Rather than being a champion for democracy across the world the way the Obama administration has tried to position itself, it stands to reason that a Trump administration will stand for “normalcy in business relations” and let other nations do what they do. I still don’t see what the US interest in overthrowing Qaddafi was, and that seems like something that Trump just wouldn’t do because the return on investment is negative “We get rid of a guy we don’t like, but then get sucked down into long term stability operations for a decade or two? Sounds like stupidity to me.”
In Europe, Russia will still push for hegemony over Ukraine, Georgia, and to some extent over the rather compliant Belarusians (who understand very well that having Moscow right on your front door means that you have to be “pro-Russian” to survive or end up like Ukraine).
In Southeast-Asia China will continue to fortify it’s defenses, those A2AD (anti-access, area denial) capabilities while also building regional and international force projection capabilities. China’s single jet fighter capable aircraft carrier will continue to be a training platform for the time being, but that will change as China builds or buys more carriers. China doesn’t want war, but it want’s to hold the same level of regional power and influence in the future that Japan held through the 1990s.
So expect the US to not stand up publicly to “human rights abuses” or openly support “pro-Democracy rebels” under Trump as the Obama administration has done. Expect a little more compromise with China and Russia on things that concern them, as long as trade can flourish I don’t see Trump trying to dictate terms unilaterally to the other two big names in world military power.