Safer America for Everyone Right Now Act or the SAFER Now Act This bill establishes new restrictions and requirements regarding the sale, transfer, and possession of firearms. Specifically, it does the following: prohibits a licensed gun dealer from transferring a firearm to an unlicensed person prior to the completion of a background check; generally prohibits the import, sale, manufacture, transfer, or possession of a semiautomatic assault weapon (SAW) or large capacity ammunition feeding device (LCAFD); requires a gun dealer to conduct a background check prior to the sale or transfer of a grandfathered SAW between private parties; requires law enforcement agencies to be notified when a prohibited person attempts to purchase a grandfathered SAW; allows Edward Byrne Memorial Justice Assistance Grant Program funds to be used to compensate individuals who surrender a SAW or LCAFD under a buy-back program; requires a person who operates a gun show to meet certain requirements (e.g., minimum age and registration); makes trafficking in firearms a stand-alone criminal offense; prohibits firearm sale or disposition to or receipt or possession by a person who has been convicted of a misdemeanor crime of stalking; and prohibits the import, sale, manufacture, transfer, or possession of a trigger crank, a bump-fire device, or any part, combination of parts, component, device, attachment, or accessory that is designed or functions to accelerate the rate of fire of a semiautomatic rifle but not convert the semiautomatic rifle into a machine gun.