The second-year tight end feels much more comfortable now.
Comfortable enough to come up behind Tom Brady, pound on the star quarterback's shoulder and embrace him after they connected on a touchdown pass for the first time.
''Caught up in the moment,'' Wright said Wednesday. ''It was a great feeling.''
Brady hit Wright for a 17-yard touchdown that gave the Patriots a 14-0 lead in their 43-17 win over the Cincinnati Bengals last Sunday night. It was one of a season-high five catches for Wright.
That performance came at an opportune time as impatient fans were wondering why the Patriots traded six-time Pro Bowl left guard Logan Mankins to Tampa Bay for Wright. After all, Wright was just a free agent wide receiver from Rutgers who signed with the Buccaneers as an undrafted free agent before last season.
''I don't really pay attention to a lot of things that have been said,'' Wright said. ''I just know once I'm in house, once I'm in the facility, I've got a job and I try to do everything I can to do my job as best as I can.''
The Bucs shifted him to tight end last season. With numerous injuries in the receiving corps, Wright caught 54 passes, five for touchdowns.
He has the potential to give the Patriots a second receiving tight end that they lacked last season after the team released Aaron Hernandez when he was arrested last summer and before he was charged with first-degree murder.
Rob Gronkowski has played all five games following offseason knee surgery and had season highs of six catches for 100 yards against Cincinnati, including one touchdown. For the first time this season, he was not on the injury report Wednesday.
''When they're out there together we've got to be able to do multiple things. I certainly can't put them on the field and just do one thing with them or else that becomes something that the defense can focus on too much and try to take away,'' offensive coordinator Josh McDaniels said. ''They both showed up, obviously, and made some plays for us, but they also did some things in the running game and other areas that helped our team.''
At 6-feet-4 and 220 pounds, Wright must block bigger linemen and linebackers. In just his second season as a tight end, it's a skill he's working on.
Instead of being able to run a few yards as a wide receiver before encountering a defensive back, he has less time and room before meeting a defender.
''A lot of guys who are playing on the other side of the ball have been doing what they've been doing their whole lives,'' Wright said, ''so it's definitely a learning curve for me to learn that technique ... and being at the right position at the right time.''
That curve may not be as great for Wright, who earned Big East All-Academic honors in 2011 when he caught 11 passes at Rutgers.
''Tim's a real smart guy. He's got a lot of experience in the passing game as a former receiver and experience from last year as a tight end in Tampa's system,'' coach Bill Belichick said.
But like the Patriots other tight ends, he had catching up to do.
Wright was obtained just 13 days before the season opener. Gronkowski didn't play in any preseason games while coming back from surgery. Michael Hoomanawanui was sidelined for most of training camp.
''We haven't really had those guys on the field as much as we would like,'' Belichick said.
But the time they have had to practice and play together has been valuable. Their next chance comes Sunday against the Bills in Buffalo.
''That, progressively, has helped us week by week,'' Belichick said.
Wright even is learning about the free-spirited Gronkowski.
''Outside of him being called `Gronk,' I didn't really know too many things about him,'' Wright said, ''but he's a great guy.''
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