Who can admit a new State in the Indian Union?

Parliament can admit a new state in the Indian Union. Article 3 of the Indian Constitution states that the Parliament may, by law, form a new state by separation of territory from any State or by uniting two or more States or parts of States or by uniting any territory to a part of any State. Also, the Parliament can – 

• Increase the area of any State
• Diminish the area of any State
• Alter the boundaries of any State
• Alter the name of any State. 

Further Reading :

• Difference between State and Union Territory
• Parliament and State Legislature

To read more about the Functions of the Parliament, check the linked article.