More than 13,000 people had registered an interest in the £30 NIC cards, although it is not known exactly how many were issued before the multimillion-pound scheme was scrapped.
CitizenCards, which cost £15 to buy and bear the PASS hologram, are recognised as valid ID by police and Trading Standards.
CitizenCard chief executive Andrew Chevis said that the organisation was also planning to discuss with the new government further ways in which it could advance recognition and use of CitizenCards. He added: "Following the demise of the NIC scheme CitizenCards and the PASS hologram will be of even greater benefit. As a result, we are delighted to offer holders of a NIC the opportunity to obtain a free CitizenCard."
The Association of Convenience Stores welcomed the move. "We will be asking Ministers to support proof-of-age cards, specifically the PASS scheme, to show their commitment to preventing underage sales," chief executive James Lowman said.