The New Zealander initially arrived in Belfast on a one-year development contract but his impressive displays last year earned him a well-deserved contract extension.
In addition to the Treviso clash, he also appeared in the opening day 28-6 triumph over Ospreys.
With the likes of Chris Henry and Iain Henderson away at the World Cup, the 26-year-old has an opportunity to impress even further in the coming weeks and it's a chance he is desperate to take.
"There are some good players around the squad and this next block of fixtures will really test our depth," Reidy told Ulster's website.
"The challenge for me is to force my way into the matchday squad on a more regular basis and get more minutes on the pitch.
"Every time I enter the field I'm determined to do everything for the team and put in performances that I can be proud of.
"I'm in my second season here. I feel like I've come on leaps and bounds thanks to the coaching staff and the players around me.
"I've learned plenty and settled in well. They are really friendly guys and I get on well with everyone."
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