Under Tier 4, you cannot work as a professional sportsperson including as a sports coach.
This means that if you fall into one or more of the seven groups below, you are restricted to playing or coaching as an “Amateur” in a charity event. "Amateur" means a person who engages in sport solely for personal enjoyment and who is not seeking to derive a living from it, which includes payments made in kind. The Tier 4 policy guidance published on 26 June 2019 states that this can include participating or coaching "in grassroots/amateur sport, for instance at and for local and community teams, as well as at your Tier 4 sponsor, and in amateur competitions and leagues, such as those organised through British Universities and Colleges Sport (BUCS)".
Definition of 'professional sportsperson'
1. You are currently providing services as a sportsperson, or playing or coaching in any capacity, at a professional or semi-professional level of sport
2. You are currently receiving, or in the previous four years have received, payment (including payment in kind) for playing or coaching. The payment also covers, or covered, all or most of your costs for travelling to, and living in, the UK
3. You are currently, or in the previous four years have been, registered to a professional or semi-professional sports team
4. You have represented your nation, national team, state or regional team within the previous two years
6. You have an established international reputation in your chosen field of sport
7. You engage an agent or representative, with the aim of finding opportunities as a sportsperson, and/or developing a current or future career as a sportsperson, or you have engaged such an agent in the last 12 months
If you do not fall into one of the groups above, you may undertake paid or unpaid sporting activities, including work placements which are an assessed part of your course.
The Tier 4 policy guidance also sets out some guidance on sports scholarships:
"In certain circumstances you may be offered a sports scholarship, to assist you in studying in the UK. If you are required to play or coach sport in exchange for receiving the scholarship, this activity is only permitted if you are studying a course at degree level or above, at a Higher Education Institution with Tier 4 sponsor status and the scholarship has been awarded for playing or coaching sport at an amateur level for your Tier 4 Sponsor or British Universities and Colleges Sport (BUCS)".
There are alternative immigration categories which permit you to work as a sportsperson and to study. For example, under Tier 2 or Tier 5 (Temporary Worker) or UK Ancestry.