Gene Roddenberry had a requirement of Will Riker
As creator of the Star Trek franchise, Gene Roddenberry had a lot of input into what happened during the production of Star Trek: The Next Generation. He had specific requirements like no conflict between the crew members and one that was especially reserved for Commander William T. Riker, one that series star, Jonathan Frakes, had a little bit of issue with.
In an interview with SyfyWire, Frakes said that Roddenberry asked him to keep the commander from smiling. Roddenberry wanted Captain Picard’s Number One to “be played with what he referred to as a Gary Cooper, Midwestern glint—not a scowl, but not smiling.” And as Frakes is a friendly guy, smiling is second nature to him so he thought he looked uncomfortable during the entire first season.
Gene Roddenberry’s rules relaxed as time went on
Fortunately, Frakes didn’t have to stay as solemn as Roddenberry wanted him to for very long. As time went on, the characters grew and evolved into their own beings, and even though you couldn’t call Riker a fun-loving guy on the show, especially when he was on duty, his sternness did ease up during the following seasons.
Some of that happened because Frakes was able to interject some of his own personality and likes into the character, such as his love of the trombone and jazz which were made a part of Will Riker. And as more time elapsed, Riker did have fun with his fellow officers, especially when playing a game of poker.
If you look back at season one of the series, there was a more solemn tone to it overall. How much of that was because of Roddenberry’s wishes we don’t know, but crew members did lighten up in later seasons with the exception of Captain Picard who maintained a sense of quiet authority and stern command at all times. It was rare to get a smile out of him so that was left up to the rest of the cast.