A video of Zouma kicking and hitting a cat went public in February.
The animal welfare act was the subject of a hearing at the court.
The brother of Zouma pleaded guilty to one offence.
Yoan filmed the incident and posted it on social media.
The addresses of the brothers have been kept secret.
The court was told that the video of the incident was filmed at the West Ham player&s home and was posted on the social media platform.
A woman who was messaging Yoan raised concern after seeing it.
Zouma threw a pair of shoes at the Bengal cat and hit it on the head.
Hazel Stevens told the court that Kurt could be heard saying he would kill it.
He admitted to causing unnecessary suffering to a protected animal.
Yoan was charged with aiding, abetting, counselling or procuring his older brother to commit an offence.
More to come.