Harrad, 34, has just finished a month on loan at Grantham Town and earlier in his career played in the Football League for the likes of Notts County, Burton Albion and Bury.
He goes in to contention for this Saturday’s game at home to high-flying South Shields, with Basford keen to end a run of three successive defeats.
Manager Martin Carruthers said: "Shaun Harrod is a great signing and we are hopeful of adding another player, also Jerry Nash, Liam Hearn and Courey Grantham will all train this week and Jack Thomas is available again after suspension, which will provide us with real quality and strength against one of the best sides in the league.
"The lads are going to have to dig deep and respond after last Saturday, we have some quality players and that needs to be shown on the pitch.
"We will work hard this week and get back to basics and show that we are a good team and get the season back on track."