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I can see the Yankees being aggressive on the starting pitching front given their weaknesses in the rotation throughout the 2015 season. At one point, all of their starters were on the disabled list and none of them could be counted on for a consistently dominant effort, although there were flashes of brilliances sprinkled throughout some starts by Michael Pineda and Masahiro Tanaka. Severino is the only bright spot in the rotation, as he is a key to the Yankees future success. He exceeded expectations since he arrived from Scranton and only had one blip against the Blue Jays where he gave up six runs in two innings earlier in September. CC Sabathia has his issues, and cannot be counted upon to be a reliable pitcher in 2016 given his age and wear, and Ivan Nova will likely be flipped this offseason for a decent right-handed bat if the Yankees could include him in a package.
This brings me to the most pressing issue the Yankees face: right handed power. The Yankees have historically had a great left-handed lineup, but the lineup is also very vulnerable against southpaws as was ever so evident in the second half following Teixeira's injury and A-Rod's bad August and September. Their lefty table-setters did not do the job, as Gardner had the league's third lowest batting average since the All-Star Game and Ellsbury was a shell of himself following an injury that sidelined him for all of June. In addition Brian McCann struggled mightily down the stretch, finishing the season with a .232 average after being as high as .275 in early July. However, McCann is a catcher and catchers wear down as the season progresses given the strenuous toll it takes on their bodies. Together, along with Gardner and Ellsbury (the $153 million man who sat in the wildcard game), these three offensive players were in large part the reason for the Yankees struggles in August and September.
The Yankees would do anything to get out from under Ellsbury's putrid contract, to which he is still committed to for five seasons (through 2020). They would like a right handed bat in the outfield to take Beltran's place after his contract ends following the 2016 season, which will likely mean that star prospect Aaron Judge will be ready to take over the right field spot, with better defense and a promising bat. If the Yankees want to package Ellsbury and eat most of his contract (which will be very tough to do), they would likely go after a Yoenis Cespedes type of player who can put fear into the opposing pitcher's eyes. However, I see this as a very unlikely scenario unless they can offload the contract of Jacoby Ellsbury.
Whatever the Yankees do this year, they will address the issues. They do not necessarily need to make a splash in the free agent market, but instead may be able to pull off some trades that are unexpected, similar to last year when they traded for RHP Nathan Eovaldi and SS Didi Gregorius who turned out to be big players for the Yankees.
You just never know what the Yankees will do, but you do know they will not sit on their hands while issues need to be addressed . This is why they are the Yankees; they will do whatever it takes to put a competitive team on the field and give their fan base something to cheer for.