12 - Broncos (DT, OT)
13* - Panthers (OT)
14* - Bears (OT)
15 - Lions (OT)
16 - Cardinals (OT)
I think there's a sincere interest for Clady by teams 13 and 14...not sure about the Broncs at 12, or any of the others listed. With so many teams in succession needing an OT (will take your word for it), makes sense for at least one to attempt to leapfrog someone, and deal with the Pats.
I won't be surprised if the Pats take Clady, as he's only one of two I think we'd consider at 7. But if protecting Brady seems to be the order of the day, I'd still trade down, acquire extra picks, and select OT Chris Williams. He's consistently ranked as the 3rd best OT overall, while some scouts feel he may be the best pass blocking tackle in the draft.
Of course the listed teams could also take Williams, or even Otah rather than trade up for Clady. My suggested scenario only works if one team is enamored with Clady, and by nature, most teams do get attached to specific players.
If Clady's gone by #7, we better hope that someone wants McFadden, Ryan, or Ellis.