His guilt and/or karma made him gray. His hair grays too quickly after he turns on Ted to just be the passage of time.

Nate’s look is also inspired by coach Jose Mourinho

I always got the impression that Nate dyed his hair in season 1 and let it slowly fade to his natural (grey) color over the course of season 2. Now I’m thinking I’m way off and it was totally the stress of the job and his parting from Ted that did it.

He didn’t age more rapidly, he just stopped dying his hair.

When he was afraid of aging he covered his grey.

When he became more accepting of aging, he stopped covering the grey.

Everyone else aged. It’s the way time works

I don’t remember where I saw it but I think Brendan Hunt was talking about how they made Nate go grey as his stress and anger got worse throughout his arc.

Stress is a killer. If you notice he started aging in season 2. It got more noticeable as the season went on, especially after he cussed out Will. I think the grey eyebrows and silver hair were an outward expression of his inner conflict