"I have to study but Aamir has to play."
Translation:मुझे पढ़ना है लेकिन आमिर को खेलना है।
Where would you put the other को?
If it's in 'I have to study', then note that मुझे can be understood to be 'मैं'+ 'को'.
To elaborate, postpositions in Hindi typically only accompany nouns. Pronouns have a case-system instead where their form is changed. A lot of the times, it is pretty evident (For example, 'आपको' is the dative-case form of आप which would be equivalent to adding the postposition को) but not always.