The Subsidiary Alliance is a policy started by Lord Wellesly and not Lord Hastings.
According to this policy, the British will give protection to any Indian ruler against external rebellions or internal attacks, on the condition that the ruler pays the British either in money or some territory. The payments cannot be made in any other form. These payments in money were huge and many rulers gave off territories rather than money.
The Subsidiary Alliance system was a method/policy introduced by Lord Wellesley to subjugate Indian powers without the cost and botheration of war. Any Indian ruler, whose security was threatened, was encouraged to seek help and enter into an alliance with the British, who promised to protect the ruler from external attacks and internal revolts.
The Indian ruler had to accept certain terms and conditions. This arrangement was known as Subsidiary Alliance.

Some Principles of the Alliances were

An Indian ruler entering into a subsidiary alliance with the British had to accept British forces within his territory and also agreed to pay for their maintenance.

The ruler would accept a British Resident in his state.

An Indian ruler who entered into a subsidiary alliance would not enter into any further alliance with any other power, nor would he declare war against any power without the permission of the British.

The ruler would not employ any Europeans other than the British, and if he were already doing so, he would dismiss them.

In case of a conflict with any other state, he would agree the resolution decided upon by the British.

The ruler would acknowledge the East India Company(Britishers) as the paramount power in India.

In return for the ruler accepting its conditions, the Company undertook to protect the state from external dangers and internal disorders.

If the Indian rulers failed to make the payments required by the alliance, then part of their territory was to be taken away as a penalty.

(the Subsidiary Alliance was introduced by Lord Wellesley, the British Governor-Genaral in India from 1798 to 1805 and not by hastings)