Complex sentence: On BBC Radio 3, he succeeded Steve Race as the presenter of the Saturday afternoon programme "Jazz Record Requests", and played requests from an international audience on "Jazz for the Asking" on the BBC World Service.
Split into simpler sentences: On BBC Radio 3, he succeeded Steve Race as the presenter of the Saturday afternoon programme "Jazz Record Requests". And played requests from an international audience on "Jazz For The Asking" on the BBC World Service.