Ward is delighted key players Nick Ward and Sam Hall will stay with the club, despite overtures from Leek, who have taken Ricky Bridge, Tim Sanders and Matt Haddrell.
Former Leek man Steve Brannan, who played for the now defunct Biddulph Vics last term, has also joined ambitious Athletic.
Ward said: "Kinsey has scored goals at every level he's been and has played with Walker before at Nantwich.
"I'm really pleased he has come here, especially with Haddrell leaving.
"I appreciate the efforts Ricky, Tim and Matt put in during their time with us, but I think overall we have a stronger squad going into next season, with more still to join."