I'm a Maths Teacher and was looking at applying for the TSP, what can I start doing now before I apply next September?

Take a look at our careers site and set up a job alert on Civil Service Jobs https://careers.hmrc.gov.uk/tax-graduates

I mean, is there anything else I can be doing to give myself a better chance when applying?

Also, is it 5 days a week for the TSP in training all at the location? I'd be commuting from Hull and wanted to know beforehand so I could plan travel.

HMRC is an office-based organisation, and colleagues are expected to spend 60% of their working time in the office. Our offices provide opportunity for interaction, collaboration which aids learning and development and a sense of community. Where the role allows it, and where the home environment is suitable, colleagues can work from home for up to 2 days a week, averaged over a calendar month (or a proportionate amount of time for colleagues who work less than full time).

To give yourself a better chance start looking at the Success Profiles well in advance. Start to make note of your experiences, skills and examples to match the various behaviours, so when the programme opens next Autumn you will be more ready with lots of examples to match up to the advert. https://www.gov.uk/government/publications/success-profiles/success-profiles-candidate-overview