Brady will be running the Arians offense. I'm sure that Brady will have plenty of input, but he is not bringing the Patriot offense to Tampa Bay. From PFT:
"Buccaneers quarterbacks coach Clyde Christensen told Bob Kravitz of TheAthletic.com that Brady has been open to learning a new system in Tampa Bay after a career in New England, and seems to fit what they are looking for.
Christensen worked with Peyton Manning in his prime in Indianapolis, and said this transition is different than when Manning went to Denver for a final act and took his playbook with him.
“You’re right, Peyton took his playbook and his way of doing things and when he looked at possible destinations in free agency, one of his priorities was to find a place where he could keep things the same,” Christensen said. “I’m sure there were some little changes, but for the most part, it was the vernacular he was used to. I think what we’ll see here [in Tampa] is Bruce’s offense with a Brady influence. Bruce wants to keep the offense the same. We did some good things last year....
Of course, Arians’ offense is significantly different than what Brady’s been running, and there will be more demands on the six-time champion to move the ball downfield more than he did a year ago. Christensen has seen nothing to suggest that’s an issue.
“I looked at every pass he threw for the last four years,” he said of Brady. “It was interesting because you had the possibility of [Drew] Brees, [Philip] Rivers, [Andy] Dalton, all those guys had a chance of becoming available, so we looked at all of them. And I’m telling you, anybody who says he’s lost arm strength, all I know is I must have missed something. Remember, they didn’t have those kinds of receivers [in New England] who could get deep. It wasn’t about anything that he couldn’t do....