As announced by the hunting association Arch Hunting, with a circular which has just been made public, the Ministry of the Interior has communicated the extension of authorizations and validity of various identification documents, moving the terms forward as required by Law Decree number 18 of 2020 (containing "Measures to strengthen the national health service and economic support for families, workers and businesses connected to the epidemiological emergency from COVID-19").
These also include the firearms license books which see their validity extended until 31-12-2020, while the hunting license is extended to 13 January. Therefore, by combining a valid identity document after December 31st hunting license you can go hunting with the same booklet until January 13th.