Under Tier 4, you cannot work as a professional sportsperson including as a sports coach.
You might need to decide whether your sports activities are professional or amateur. The Immigration Rules provide a definition:
'“Professional Sportsperson”, is someone, whether paid or unpaid, who :
is providing services as a sportsperson, playing or coaching in any capacity, at a professional or semi-professional level of sport; or
being a person who currently derives, who has in the past derived or seeks in the future to derive, a living from playing or coaching, is providing services as a sportsperson or coach at any level of sport, unless they are doing so as an “Amateur”'.
'An “Amateur” is a person who engages in a sport or creative activity solely for personal enjoyment and who is not seeking to derive a living from the activity. This also includes a person playing or coaching in a charity game.'
This means that you can work as a sportsperson with Tier 4 immigration permission only if you are not providing services at a professional or semi-professional level, and if you do not make, have not made, and do not intend to make a living from playing or coaching at any level, unless you meet the definition of an 'amateur'. The definition of 'amateur' implies that you can have made a living from sport in the past or plan to do so in the future but are not intending to do so now, and it includes participation in a charity game. If you are not sure if you can meet this definition, check with the sporting organisation concerned and/or your education provider.