The guidance on Grassroots sports and physical activity has been updated today to clarify the situation with personal training and exemption for under 18 activities as follows:-
In tier 3 areas: people should not take part in any indoor sport or physical activity with people from outside their household. This includes indoor team and individual sports, training sessions and exercise classes.
Personal training is permitted for 1:1 sessions only (unless all participants are from the same household or support bubble), and should not take place in private houses. Gyms and sport facilities will remain open, but group activities are not permitted (unless the group consists of a single household or bubble). Contact combat sports are not permitted.
There are exemptions to the limitations on organised indoor sport for people with disabilities, sport for educational purposes and supervised activities (including sport and physical activity) for under-18s, which can continue with any number of participants. This includes young people who were under 18 on 31 August 2020, even if they turn 18 during the remainder of the academic year.
The updated guidance can be found here: https://www.gov.uk/guidance/coronavirus-covid-19-grassroots-sports-guidance-for-the-public-and-sport-providers