subject to
subject to {adj. phr.}
1. Under the government or control of; in the power of.
The English colonies in America were subject to the English king.
The principal and the teachers of a school are subject to the school board.
2. Likely to get or have; liable.
John is in rather poor health and is subject to colds.
The western plains are subject to tornadoes.
3. Depending on some change, happening, or need.
The company and the union agreed that the workers' wages should be subject to changes in the cost of living.
Agreements made by the President with other countries are subject to the approval of the Senate.
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Source: A Dictionary of American Idioms