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 which, since 11 January 2018 says:
'A “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 who the Secretary of State has reason to believe is seeking 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” in a charity game'.
"Amateur" is also defined:
'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'.
'In the definitions of “Amateur” and “Professional Sportsperson”, “derive a living”, “paid” or similar references include payments made in kind'.
This means that you must not work as a sportsperson with Tier 4 immigration permission if you are playing or coaching at a professional or semi-professional level. You must also not work as a sportsperson if you have ever made, intend to make, or could be suspected of wanting to make a living from playing or coaching at any level, unless you provide services as a sportsperson or coach as an 'amateur' in a charity game. Receiving 'payments in kind' can be regarded as 'deriving a living'. If you are not sure if you can meet this definition, check with the sporting organisation concerned and/or your education provider. Information provided by GBSport may also help you to decide if you risk undertaking work as a professional sportsperson.