Jimmy G + Nate Solder + 2018 4th round pick to CLE
#33 (2017), #52 (2017), LT Joe Thomas + conditional 3rd round pick in 2018 (rising to 2nd round if JG starts 10-12 games, 1st round if the Browns make the playoffs) to NE
Solder has one year remaining on his current contract, with a cap hit of $11M. Trading him creates a ~$4M dead money hit on the 2017 cap. Thomas is owed $8.8M in salary for two more seasons (2017 & 2018) - his remaining bonuses would seem to create no dead money cap hit, but the Browns might need to pay out his remaining $3M in bonuses. This would result in the Patriots adding ~$2M to their 2017 cap but also (potentially) push off any need to address LT this season in the draft or spend real money on a Solder extension/bonus.
JG nets two current year 2nd round picks, as well as a (likely) third 2nd rounder next season. Cleveland adds two impact players in the first round, gets their QB1 of now and future, and only slightly downgrades their LT spot. They can more than afford to extend the younger Solder after 2017 if he's amenable.
Thomas remains one of the best LT in the NFL; Solder is good - Thomas is better. And while Thomas is older, he also has yet to show any signs of decline AND he pushes off the need to draft a potential replacement for Solder OR spend a lot of real money (and cap money) on a Solder extension in 2017. They certainly could address the position in the 2017 draft if they wanted, but with the extra year, they would not need to draft a tackle this year.
In this scenario, they almost certainly trade down and/or out of 2017's first round - banking another future 1st or 2nd in return in 2018 or 2019. Further, they own the catbird's seat on the 2nd round, possibly getting even more value from some team looking to move up for DeShaun Watson or another player at the top of the round. In any trade down (either 32 or 33), they would also add a few later round picks (like an extra 4th in 2018) - which also bolsters the cupboard and mitigates the pick sent to CLE as part of this trade.
On draft day, the Pats would have Joe Thomas (All-Pro quality LT), plus #32, #33, #52, #64, #96 in the first three rounds, plus an extra high round pick in 2018.