The establishment of a new All-India Service requires Parliament to act upon a specific resolution initially adopted by the:

The correct option is Rajya Sabha.

Step-by-Step Explanation:

1. Constitutional Provision:
Under Article 312 of the Indian Constitution, the Parliament of India is empowered to create one or more All-India Services (such as IAS, IPS, or IFoS) common to both the Union and the States.

2. Role of Rajya Sabha:
Because All-India Services affect the administrative structure of the states, the power to initiate the creation of such a service rests uniquely with the Rajya Sabha (Council of States), which represents the interests of the states at the national level.

3. Specific Resolution Requirements:
The process must begin with a resolution passed by the Rajya Sabha supported by not less than two-thirds of the members present and voting, declaring that it is necessary or expedient in the national interest to create such a service. Once this resolution is adopted by the Rajya Sabha, Parliament can enact legislation to establish the new service.