Wright, 23, arrived at the Don Amott Arena in December having had spells with Matlock Town and Grantham Town earlier in the season.
He said: “I am buzzing to have re-signed again for a further year, I knew as soon as we spoke about it, it’s the right thing for me to do!
“The club’s been great with me since I arrived from the Gaffa, lads and to all the people behind the scenes! Looking forward to getting started as soon as we can.”
Wright scored four goals in 28 appearances in all competitions last season.
Manager John McGrath said: “I am absolutely delighted to get Wrighty re-signed again for the upcoming season. He’s a fantastic footballer, an excellent competitor with a winning mentality and an unbelievable character to have at the football club.
“With a full pre season under his belt I am expecting a massive impact and contribution from him.”
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