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In principle, no relation between the two. Imperialism is the policy of extending one's authority or rule by acquiring control over other territories or nations, as was once done by the British. While modernity is just the state of being modern for anything.
I agree with A_clan, however, it could be argued that imperialism is extending one's rule by force, by aquiring territories... and in the modern era a nation can extend its rule through economic means. You could argue, for example, that Germany does not rule Greece, (it doesn't) but Germany is now able to dictate a number of things Greece has to do because it bailed them out. Even stronger, the countries that have been bailed out by the WTO, on the basis of several things they have to do in their countries, like cut funding to education etc. You can also look to the US and Latin America, how US props up some leaders and gets economic benefits in return.