Is there any compulsion that Hajj will become fard on a person only after zakat becomes fard on him?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

Hajj is an obligation on whoever is able to perform it whether or not he is obligated to pay Zakah on his wealth. Indeed, there is no correlation between being able to perform Hajj and being obligated to pay Zakah. It might be that a person is obligated to pay Zakah on his money but he is not able to perform Hajj. Contrarily, a person may be able to perform Hajj while he is not obligated to pay Zakah on his wealth because a whole lunar year has not yet elapsed, or due to possessing non-Zakatable money, or because Hajj does not require from him spending much money, like a person who lives in Makkah, for example.

For more benefit on the financial ability that renders one obligated to perform Hajj, please refer to Fatwa 85739.

Allaah Knows best.