How do I extend a TypeScript class definition in a separate definition file?

If you don't control the original definition file, and can't make adjustments to it, then unfortunately, what you're trying to do isn't supported currently in TypeScript. An interface in TypeScript is the only construct that allows reasonable extensions as it is only a compile-time/syntax check and not a run-time operation.

You cannot extend a class in TypeScript with new functionality using only TypeScript (and expecting code-completion/Intellisense to work as expected). You could of course add the functions to the prototype for the CircleMarker class, but they would be unavailable to Intellisense and would fail to compile unless you use a type assertion.

Instead of using any, you should be able to use an interface with the type assertion:

declare module L {
    export interface CircleMarkerEx {
        bindLabel(name: string, options: any): CircleMarker;
    }
}

Then:

var cm = <L.CircleMakerEx> circle.bindLabel("name", {});

Thankfully, it doesn't add any run-time overhead, just a bit of extra typing (pun intended!).

There have been suggestions for things like "mix-ins" on CodePlex, but they have not been implemented. Even the mix-in suggestions would not be entirely straightforward to use, and wouldn't work well for libraries that weren't entirely written in TypeScript (as it would be too easy to have JavaScript code that simply could not be safely constructed for example with a mix-in).

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You can't do that with the class keyword. There is a feature request you can vote on here : https://typescript.codeplex.com/workitem/917

You can however mimic classes using interfaces as shown in the workaround (https://typescript.codeplex.com/workitem/917) for the issue. In your case

declare module L {
    function circleMarker(latlng: LatLng, options?: PathOptions): CircleMarker;

    declare var CircleMarker: CircleMarkerStatic;
    export interface CircleMarkerStatic{
      new (latlng: LatLng, options?: PathOptions): CircleMarker;
    }

    export interface CircleMarker {
        setLatLng(latlng: LatLng): CircleMarker;
        setRadius(radius: number): CircleMarker;
        toGeoJSON(): any;
    }
}

and extend it

declare module L {
    export interface CircleMarker {
        bindLabel(name: string, options: any): CircleMarker;
    }
}

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This is what I tried and it feels relatively comfortable for me

declare module L {
    export class CircleMarkerEx {
        constructor(source: CircleMarker);
        public bindLabel(name: string, options: any): CircleMarker;
    }
    export function ex(cm: CircleMarker): CircleMarkerEx;
}

where CircleMarkerEx and ex can be defined as

class CircleMarkerExtender extends CircleMarker {    
    public b() {
        return `${this.a()} extended`;
    }
}
CircleMarker.prototype = Object.create(CircleMarkerExtender.prototype);
CircleMarker.prototype.constructor = CircleMarker;

export function ex(cm: CircleMarker) {
    return cm as CircleMarkerExtender;
}

then

let cm = ex(circle).bindLabel("name", {});

but it is still a little strange

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Is this possible?

declare module L {
    export class MyCircleMarker extends CircleMarker{
        bindLabel(name: string, options: any): CircleMarker;
    }
}

And then define your CircleMarker instances as MyCircleMarker

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Edit: this answer is off topic. It talks about interfaces and not classes like asked

I didn't have any problem extending a TypeScript (v3.6) external type definition.

Example with google.maps.Marker type definition:

// File types/googlemaps-marker-hello.d.ts or
// whatever file name you like, it doesn't matter
declare namespace google.maps {
  interface Marker {
    hello: string;
  }
}

// Later on inside src/MyCode.ts
const marker = new google.maps.Marker();
marker.hello = 'Hello, World!';

You don't have to modify your tsconfig.json: it just works.

It's the way DefinitelyTyped works

See https://github.com/DefinitelyTyped/DefinitelyTyped/blob/edb4917e1bbd0d860b51e7806775cb505f858e36/types/webpack-dev-server/index.d.ts#L206-L211:

declare module 'webpack' {
  interface Configuration {
    devServer?: WebpackDevServer.Configuration;
  }
}

webpack-dev-server type definition extends webpack type definition. If you use @types/webpack and not @types/webpack-dev-server you won't have the devServer property.

Another example:

declare namespace NodeJS {
  interface Global {
    hello: string;
  }
}

global.hello = 'Hello, World!';

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For those looking for the new/currently documented solution is found in:

https://www.typescriptlang.org/docs/handbook/declaration-merging.html#module-augmentation

I have used this to extend the prototype for google-protobuf generated classes to add additional predicates.

import { CgMessage, CgType } from "./CgProto";
declare module './CgProto' {
  interface CgMessage {
    expectsAck(): boolean 
  }
}
CgMessage.prototype.expectsAck = function() {
  return [CgType.send, CgType.join, CgType.leave].includes(this.type)
}

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