HONG KONG—The arrest of veteran pro-democracy figures has stirred anger among supporters of a protest movement that has stayed off the streets during the coronavirus pandemic and spurred calls to restart demonstrations this summer.

On Saturday, Hong Kong police arrested more than a dozen pro-democracy lawyers and activists. More than 7,500 people have been arrested during the course of the protests that rocked the city for much of last year, but many of those have been for alleged acts of violence and vandalism. Saturday’s...