If you are staring at the television in a fascinated way and you simply cannot look away, this is an example of a time when you stare intently at the television.
He listened intently for a few minutes.
He looked up and studied her face intently for a moment.
He was watching her intently again.
She tapped her earpiece, listened intently, and responded with a few words.
Dron looked intently at the princess while she was speaking.