The four UK farm unions have called for frictionless, tariff free trade with the EU after Brexit.
They have said a customs union is the best way of achieving it.
If that does not happen there is likely to be an economic impact on UK livestock producers, the joint unions said.
The organisations, including the Ulster Farmers' Union (UFU), have said "sensitive" sectors like beef and sheep may need trade protection.
They are concerned that a cheap food policy could lead to imports of produce from around the world.
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They say if farmers in Northern Ireland are to remain competitive, the imports must be produced to the same welfare, environmental and traceability standards.
The call for tariff free access is particularly important for Northern Ireland's lamb sector.
A significant proportion of it is processed in the Irish Republic and shipped to markets in places like France and Spain.
The joint position was adopted by the UFU and the National Farmers' Union of Scotland, England and Wales.
They also want the government to open new markets for red meat.