Using Collectors.toList instead of forEach and a new ArrayList
This is one way using flatMap and Collectors.toList():
public List&lt;SearchSuggestion&gt; suggest() {
   return someService.findAll().stream()
            .flatMap(wl-&gt;wl.getWatchlistItems().stream())
            .map(wli-&gt;mapToSearchSuggestion(wli.getInstrument()))
            .collect(Collectors.toList());
}

However (since this is Code Review) the method mapToSearchSuggestion seems more appropriate to be in the class Instrument. If you can move it there then the function becomes:
public List&lt;SearchSuggestion&gt; suggest() {
    return watchlists.stream()
            .flatMap(wl -&gt;wl.getWatchlistItems().stream())
            .map(WatchlistItem::getInstrument)
            .map(Instrument::mapToSearchSuggestion)
            .collect(Collectors.toList());
}

Instrument class:
public class Instrument {
    //...
    public SearchSuggestion mapToSearchSuggestion() {
        return SearchSuggestion.builder().symbol(getSymbol()).build();
    }
    //...
}