HBO is associating with Apple for the start of its much anticipated Internet streaming service, uniting two premium brands from the media and technology worlds in a quest to reinvent the way people watch television. Called “HBO Now,” the service does not require a traditional TV subscription and will be available exclusively on Apple devices when it makes its debut in early April, the companies announced on Monday during an Apple product event at the Yerba Buena Center in San Francisco. Timed to coincide with the start of the new season of its most-watched series, “Game of Thrones,” the service will cost $14.99 a month and offer all of HBO original programming, past and present, as well as its movie offerings. People who subscribe to the service in April through Apple will receive the first month free. The exclusivity with Apple lasts for three months. HBO also is in talks with other distributors, including traditional TV providers and digital partners.