How can I define an array of objects?

You are better off using a native array instead of an object literal with number-like properties, so that numbering (as well as numerous other array functions) are taken care of off-the-shelf.

What you are looking for here is an inline interface definition for your array that defines every element in that array, whether initially present or introduced later:

let userTestStatus: { id: number, name: string }[] = [
    { "id": 0, "name": "Available" },
    { "id": 1, "name": "Ready" },
    { "id": 2, "name": "Started" }
];

userTestStatus[34978].nammme; // Error: Property 'nammme' does not exist on type [...]

If you are initializing your array with values right away, the explicit type definition is not a necessity; TypeScript can automatically infer most element types from the initial assignment:

let userTestStatus = [
    { "id": 0, "name": "Available" },
    ...
];

userTestStatus[34978].nammme; // Error: Property 'nammme' does not exist on type [...]

What you have above is an object, not an array.

To make an array use [ & ] to surround your objects.

userTestStatus = [
  { "id": 0, "name": "Available" },
  { "id": 1, "name": "Ready" },
  { "id": 2, "name": "Started" }
];

Aside from that TypeScript is a superset of JavaScript so whatever is valid JavaScript will be valid TypeScript so no other changes are needed.

Feedback clarification from OP... in need of a definition for the model posted

You can use the types defined here to represent your object model:

type MyType = {
    id: number;
    name: string;
}

type MyGroupType = {
    [key:string]: MyType;
}

var obj: MyGroupType = {
    "0": { "id": 0, "name": "Available" },
    "1": { "id": 1, "name": "Ready" },
    "2": { "id": 2, "name": "Started" }
};
// or if you make it an array
var arr: MyType[] = [
    { "id": 0, "name": "Available" },
    { "id": 1, "name": "Ready" },
    { "id": 2, "name": "Started" }
];