In 2015, the Yankees had 11 position players over the age of 30. It is likely we will never see the likes of Stephen Drew or Garrett Jones again (really hoping we don't see the former), but the other nine, for the most part, were integral parts of the Yankees' roster this past season. Alex Rodriguez, Mark Teixeira, Carlos Beltran, Brendan Ryan, Brian McCann, Chase Headley, Brett Gardner, Jacoby Ellsbury, and Chris Young were very important to the success of the club, and they'll likely be relied upon next season. That isn't a fantastic thing, really.
Older rosters are not necessarily bad rosters. The Yankees throughout their dynasty years were always among the older teams in the league, and they continued to be successful because they constantly supplanted the very old with the slightly younger free agents to fill in the gaps. There were youngsters among them (Phil Hughes, Robinson Cano, David Robertson, etc.), but the teams of ten years ago really relied upon the older players. That was fine--then! Back then, players over 30 had a higher level of performance than today, so it was very possible to make this model work. Today, that isn't fully the case.
Other than Didi Gregorius, every starting position player will likely decrease in talent level. This isn't because of some more moral failing or because they failed to be in the best shape of their lives, it's just because they're going to be a year older. The general sabermetric rule of thumb is that players over 30 lose five runs of value per year, meaning that the Yankees would lose about four or five wins off their true talent without doing a thing. That is precisely the difference between being a wild card team and staying home.
How could the front office push against this tide? The obvious answer, and the one that is easiest to understand, is to sign a marquee free agent. David Price, Zack Greinke, Ben Zobrist, Justin Upton, and Jason Heyward will all be free agents, and that is a pretty loaded class. If they were to get any of the first three, it would easily recoup the losses of the aging process, and it would likely replace a replacement level performance (if you're not too optimistic about second base).
As I said, that's the "easy" decision. It's the one the front office has made, and it's mildly successful. The only problem, though, is that eventually you run out of space to do this. The Yankees are generally locked in at almost every position, so if you decide to spend on Zobrist this year, what do you do in 2017? You essentially face the same problem once again, and next time without a clear solution.
Another solution is via the trade, and this has already been pretty successful. Acquiring Gregorius is now considered a fantastic move, and that's because of this idea of upside: not only does he provide you with above-average performance at a premium position, but he is also young and improving, meaning that you won't get this natural and inevitable decline. There's no guarantee he'll continue to be good, but the breakdown of his body won't be the cause. Many have floated around the idea of trading Brett Gardner, and that's a risky one. He's an above average player, and that may just supplant one problem with another.
This is not new to many Yankees fans. The idea of the "wrong side of 30" is a common trope among Yankees fans' rhetoric, and it's largely rooted in the fantasy of creating a new dynasty era: if only we had a core of players under 30, they say, then the Yankees will be set for years to come. That is not going to happen. The team was never filled with younger players--even in the dynasty years--and free agents will always be a key role to the Yankees' model of roster construction.
I do think, though, that the idea of "tweaking", "retooling", or whatever phrase you use, is really applicable to this predicament. You likely won't replace half of your roster with younger and better players, but if the Yankees trade for a younger player and become younger in one spot, and maybe acquire a free agent somewhere else, you at least chip away at the inevitable tide of an aging roster. I could come up with some bad trade ideas as to what that could be, but it's really too early to speculate. All that can be said now is that this team won't be as good as it was in 2015 just by virtue of getting older, and standing pat should be unthinkable. I think the strategy will be similar to last year--mid-level free agent signings and trades for younger players, and that would likely be ideal. The short term solution to this problem is by signing a big free agent, but it's merely tabling an issue they've been dealing with for a long time.