despite; without regards to ~
This pattern expresses doing something without regard for or despite another situation or expectation.
をよそに is a written-style pattern used to describe a situation where someone acts without caring about something that would normally be a concern, or despite what others think or expect. It often carries a nuance of criticism or indifference, and is common in news reports and formal writing rather than casual conversation.
Think of it as saying 'without paying attention to ~' or 'in defiance of ~'. The thing being ignored is placed before をよそに. For example, 親の心配をよそに means 'ignoring the parents' worries'. The subject of the sentence does something that contrasts with that ignored thing.
This pattern is quite formal and literary. In everyday speech, you would more likely use ~のに構わず or ~を無視して. But at N1, you need to recognize and use it in appropriate written contexts.