Clare, who finished as top scorer in the Conference last season for champions Chester, was determined to quit the club when his contract exired at the end of this season.
Rush said: "Daryl told me he wasn’t going to renew his contract just days after I had taken over because he had an agreement to rejoin his ex-manager at Boston United.
"Daryl’s contract was up at the end of the season but I was willing to appreciate his wishes.
"Daryl has done well for Chester and I was always going to be honest with him. I know his departure will leave us short, but I've now got to look to the future interests of Chester City."