Complex sentence: The recipient must either be British; or reside and play a significant amount of their sport in the United Kingdom, with their core achievements that year being in the UK, and not with a non-UK national team.
Split into simpler sentences: The recipient must either be British, or reside and play a significant amount of their sport in the United Kingdom. Their core achievements that year must also be in the UK, and not with a non-UK national team.