Lindup had been with the Nottinghamshire piling specialist Van Elle for two years and also acted as company secretary.
He is the third director to leave the company since it floated on the stock exchange raising £40m.
Chairman Michael Ellis and deputy group chairman Vic Hanley both retired from the business at the turn of the year.
Lindup’s operational responsibilities will be absorbed by senior colleagues on the executive management team.
Paul Pearson, Chief financial officer, will replace Lindup as company secretary where he focused on the contractual, compliance, insurance, negotiation and legal elements of the group’s operations.