A longtime associate of Mr. Ailes, who spoke on the condition of anonymity, said Mr. Trump thought he was “getting Roger,” who built Fox with a keen eye for aggressive political strategy, in his hire. But Mr. Shine, according to his critics, has shown little understanding of the conservative media beyond the cable news ecosystem and his former network — the one place where the president does not need much assistance, and where Mr. Shine has few remaining admirers…

To his friends and allies, Mr. Trump wistfully brings up Hope Hicks, his most successful communications director, who departed nearly a year ago. Ms. Hicks had the president’s trust in a way that only a few remaining aides do, and she was generally seen as among the small number of people who could suggest to Mr. Trump that he hold back from indulging in some of his public relations whims.

Since arriving, Mr. Shine has chosen to become useful to Jared Kushner and Ivanka Trump, the president’s son-in-law and eldest daughter. At one point, Mr. Shine tried to help craft a network special for a planned trip by Ms. Trump to Africa, which has been postponed amid the government shutdown.