There are about 6 positions on the field worth spending a lot of money on by default. They are:
QB
LT
RT
CB1
CB2
FS
This is because they never come off the field and are very in demand, due to being important positions that are hard to fill.
On offense last year, the only players who played more than 90% of snaps were the offensive linemen. Obviously Brady would also be in that group if he wasn't suspended 4 games.
Edelman (WR1) and Bennett (TE1) played 78% of snaps.
On defense, only McCourty, Butler, and Chung played over 90% of snaps. Ryan was at 86%, as I believe he was "benched" a couple games as the Pats tried out Rowe, Coleman, and the Joneses to find their best lineup.
Hightower was the front 7 player with the most snaps, 68%.
IF the Patriots can sign Butler for Gilmore money long-term, they will do it, regardless of having already paid McCourty and Gilmore. Nobody else they could sign is better than Butler, at a more important position than CB, who will project to play more snaps.