Shares of Robinhood Markets Inc. moved higher after hours on Wednesday after the trading app reported first-quarter results that were better than expected — even as trading activity remains muted when compared to last year.

But in Robinhood’s HOOD latest efforts to reverse that trend with new products — including things like IRAs and forays into advisory services and futures offerings — the company said that it would launch a new 24-hour trading service next week, called 24 Hour Market, that would allow around-the-clock stock...