Alex Shane has already touched on the topic of trading for a DT in his article Life Without Wilfork: Will the Patriots Trade for a Defensive Lineman? posted here on PatsPulpit. A good read, which helps to make clear how unlikely a trade for a worthwhile DT is to happen. Any team that might be willing to trade would ask a high price, a draft pick being much more likely than any player... because the only teams that would be willing to make that type of trade is thinking about the future, and will want picks for the future, not some player the Patriots feel they can do without.
The Patriots would have to weigh the value of the player traded for, how talented, how many years remain on his contract, how expensive that contract is, against the value of that pick, and the players they could target in next year's draft, that would be working on a rookie contract.
A more likely, CAP friendly, and draft friendly scenario, would be for them to sign a veteran FA that is currently unemployed but in years past has started for other NFL teams as a 3-4 NT. Belichick said recently that there aren't those types of players just standing around on the street corner.
Truth be told... there is more than one essentially doing just that. The Patriots just have to be willing to pull the trigger and pay one of them well for six months worth of work.
To be clear, the Patriots don't need just any old DT or DE type of player, the Patriots need a NT… a big beefy body that can hold their position, and give them a solid 20-25 snaps during each game… it would be a huge boon to the rest of the defense, especially the D-linemen and ILBs that will be working overtime to make up for Wilfork’s loss.
Some of the veteran FA players that can step in and fill that role are:
Ma’ake Tu’amelie Kemoeatu 6’5 345 age 34 was a disruptive force for the Ravens last year in their playoff run. He may even be a very serviceable player if he has kept his weight down and didn’t go straight into feasting mode after winning the SB.
Casey Hampton is 6’1 and 325, at age 36 he doesn’t have much tread left on his tires, but he is familiar with 3-4 NT duties having served on the Steelers for many years in that role. He has a similar body type to Wilfork, and if used sparingly could probably be serviceable in a reserve/sub role.
Ron Edwards is 6'3 320 age 34, a former Panther, Ron, and the remaining FA DTs out there, fall more along the lines of DT/DE types, and are typically either very injury prone (IE - Ty Warren) or fringe talents (IE - Amobi Akoye) that never panned out.
I suspect the Patriots will run with what they have on the roster, and try to make do, this in turn will prove to be untenable, after the Bengals and Saints prove themselves more than capable of attacking the line with the run, forcing the Pats to commit extra attention to closing the gaps.
The Bengals will begin to expose the lack of depth and size along the D-line, and then Brees and the Saints will tear into them, dissecting the field, as the linebackers are forced to play the LOS rather than the middle of the field, after the Saints rip off a couple lengthy runs.
The Patriots then will be willing to concede that they don't have the manpower on the roster, not if they want to be able to compete seriously down the stretch, and in the playoffs. They will have to sign a veteran that is now 'standing on a street corner' to aid the D-line. Obviously none of these older options will have the athletic skills or endurance Wilfork has, but at least they will be able to anchor the middle.