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To render an animated .gif using DirectX11, you need to follow these steps:

1. Load the .gif file into memory using a suitable image library such as FreeImage or DevIL.

2. Extract each frame of the .gif file and store them in a collection, along with their corresponding timing information.

3. Create a texture resource for each frame and upload the image data using DirectX11 functions like ID3D11DeviceContext::UpdateSubresource.

4. Create a vertex buffer and index buffer to define a quad that covers the entire screen.

5. Set up a pixel shader to sample the texture containing the current frame and output the color to the screen.

6. Set up a timer to update the current frame at the appropriate times, based on the timing information extracted from the .gif file.

7. On each frame, bind the appropriate texture, draw the quad using the vertex and index buffers, and present the backbuffer.

8. When the animation is complete, release all resources used for rendering.

Note that there are many different ways to implement a GIF renderer in DirectX11, and the exact details will depend on your specific requirements and programming style. This approach is just one possible example of how you could tackle the problem.