Which form of imperialism involves a foreign power that has exclusive trading rights with a smaller country?

Sphere of Influence.

Explanation:

Sphere of Influence is an imperial strategy that influences a smaller country to surrender exclusive investments or trading privileges to a bigger foreign power.

Today, Sphere of Influence is a tool of foreign policy where powerful countries tries to strike an agreement with a weaker country to disintegrate it's political, economical and military powers to the powerful one.

The Navigation Acts of 1651 passed by the English Parliament during the period of imperialism and colonialism is similar to the concept of Sphere of Influence. The Acts prohibited foreign ships from transporting non-English goods to England or its colonies. It only allowed English vessels to carry English trade to its colonies.