I don't think that the front seven is particularly weak at all in terms of pass-rush potential, or even at the "DE position" taken in isolation (however that may be defined). I'm really not feeling any desperate, "OMG! We're DOOMED!!", need to immediately sign a proven DE/edge-rusher.
BB may yet add a veteran player to the front seven, but likely more for depth, I think, and more likely an OLB-type to possibly replace McLellin (who hasn't practiced in a long, long time for reasons unknown).
In 2016, the Pats kept 4 LB, 3 DT, 4 DE plus two non-contributing special teamers (Grissom and Mingo) for the front seven (13 total players).
Not including Rivers (IR), Keionta Davis (likely Reserve/NFI), or potential PS-types Kidder, Hamiltion, Kilgo, Augusta, here's the "menu" of front-seven players currently on the roster (along with my take on their positional/role versatility):
Branch (NT-DT)
Brown (DT, some edge rush)
Valentine (DT, some edge rush)
Guy (DT/DE)
A. Butler (DT/DE)
Flowers (DE, some interior rush)
Wise (DE, some interior rush)
Langi (DE/OLB - ST), Grissom (DE/OLB - ST)
Hightower (ILB/OLB/DE)
Van Noy (ILB/OLB/DE)
Harris (ILB)
*Roberts (ILB) ... bruised ribs, practicing with red jersey
*McLellin (OLB/DE/ST) .... unknown injury, lengthy practice absence
Bates (LB - ST), Freeny (LB - ST)
That's 16 players.
It seems to me that the Pats can extract 13 pretty solid front-seven players from that list, including covering the ST snaps of Grissom and Mingo.