if someone or something is subject to something, especially something bad, it is possible or likely that they will be affected by it:
All flights are subject to delay.
Prices are subject to change.
if something is subject to something such as approval#, it depends on that thing happening before it can happen:
The funding is subject to approval by the Board of Education.
if you are subject to a rule, law, penalty etc, you must obey the rule or pay an amount of money:
Violators are subject to a $100 fine.
3 [only before noun] formalPG
a subject country, state, people etc are strictly governed by another country: