The 25-percent import tariff that the Chicken Tax imposes on foreign trucks essentially makes the things all but impossible to sell one profitably in the US, which lends a distinct advantage to domestic pickups. Both the Trans-Pacific Partnership with 12 counties and Transatlantic Trade and Investment Partnership with the European Union would finally end the charge. According to Automotive News though, don't expect new pickups to flood the market, at least not immediately. These deals might roll back the tariff gradually over time, and in the case of Japan, it could be as long as 25 years before fully free trade. Furthermore, Thailand, a major truck builder in Asia, isn't currently part of the deal, and any new models here would still need to meet safety and emissions rules, as well.
Automotive News gauged the very early intentions of several automakers with foreign-built trucks, and they weren't necessarily champing at the bit to start imports. Toyota thinks the Hilux sits between the Tundra and Tacoma, and Mazda doesn't think the BT-50 fits its image here. Also, VW doesn't necessarily want to bring the Amarok over from Hannover. There is previous precedent for companies at least considering bringing in pickup trucks after the Chicken Tax's demise, though.
The Pacific free trade deal could be done as soon as this fall, while the EU one is likely further out, according to Automotive News. Given enough time, the more accessible ports could allow some new trucks to enter the market.