Is Universal Basic Income compatible with free international trade? If one country introduces UBI, what prevents other countries from taking advantage of that and supplying cheaper (no need to finance a UBI scheme!) goods to the original country and outcompeting the local industries? Does UBI automatically mean high international trade tariffs?
There is nothing to prevent other countries "taking advantage" of an export market's UBI.  However, I don't think that that implies a country introducing a UBI would need to increase tariffs, and I have never heard this being advocated.

Since UBI hasn't been implemented on a large scale, there is little compelling evidence on what its effects will be, but a lot of speculation on what they might be.

First, it is important to observe that countries' cost bases already differ a lot in terms of firms' tax burdens and unskilled wage rates.  Countries with high taxes and high wages don't typically sustain them through protectionist tariffs.

Second, it is suggested that UBI may lower a lot of government costs, so that the impact on firms' tax burden would not be as large as you might expect.  For example, UBI would replace many benefits (e.g. job seeker and housing benefits) reducing administration costs, especially for means-tested benefits.  It is argued that it would reduce physical and mental healthcare costs related to poverty, which could be particularly important in countries like the UK that have free universal healthcare alongside substantial poverty.

Third, it is unclear what effect a UBI would have on wages.  Since workers' basic cost of living is (at least partially) covered, it is possible that wages could fall.  There would certainly be a political argument for reducing the minimum wage.  Depending on how the cost of UBI is distributed, this could more than offset the tax burden on firms.  It is also well established that a lot of traditional benefits result in very high effective marginal tax rates on part-time work (as earned income is offset by reduced benefits); a UBI is likely to improve the financial incentive for unemployed people to do small amounts of work in a lot of countries, even if wages were somewhat lower.

Finally, it is largely unknown how UBI might affect a country's comparative advantage and productivity.  For instance, some (not all) suggest that UBI would drive innovation by giving people the time and space to pursue an invention or start a business under less financial pressure.  This would lead to more value-added jobs, which is how countries typically manage to compete internationally while sustaining high wages and tax rates.