What anime is this girl kicking someone from? I found this image on an AMV called ♪ Clarissa ♪ at https://www.youtube.com/watch?v=Gje-xf8liWM. The girl appears at 1:43 in the video. I think she might be from Kiddy Grade, but I'm not sure.
Wow, this was (and is) a hard one to find but you made me curious!

TL;DR: It's Kiddy Grade.

The character pictured is indeed Éclair from Kiddy Grade. She normally looks like this.



However, this is a younger version of her, and it's really hard to find information on where she comes from - I wanted to find an episode number she appears in, but couldn't track one down, or even a proper screenshot.

This was the best I could do: via some reverse-image searching with various terms, I found this image, which has a filename equating to 'Éclair in Star Year 0318 - Kiddy Grade'. 



It's pretty believable that this is the same character as in the screenshot, and you can see from the earrings that she may well have some relation to Éclair. I tried to find more pictures similar to this one that would provide more information, but though there are a few, they don't really help much.

On a whim, I went on pixiv and was able to find this in the Kiddy Grade tag:



Credit to this artist. I think you'll agree this is the same character. The picture is entitled '幼エクレール', or, in English, 'Young Éclair'.

Anyway, I think this has to be from Kiddy Grade, and hope this clears up why. She definitely doesn't look like this for most of the series though! If anybody who's actually watched the series would like to provide more details that would be great, but anyway, hope this helped.