Any person upon becoming the owner or keeper of any unlicensed dog of the age of six months or older shall cause such dog to be licensed within thirty days thereof until the thirtieth day of the ensuing June in the manner and subject to the terms and conditions provided in § 22-338. If the new owner has written proof of purchase or transfer and the license is obtained within thirty days, he shall not be required to pay any penalties as provided by said section for failure to secure a license for a dog over six months of age. Any person becoming the owner of a licensed dog shall present the license and tag of such dog to the town clerk of the town in which he resides and, for a fee of one dollar, such town clerk shall issue, in lieu thereof, a new license and tag, which shall be recorded in the name of the new owner. Such town clerk shall retain the old license and tag in his possession.