Where does Reacher show up?
In the finale, "Touched". Neagley's father, Calvin, has died, and Reacher arrives at the funeral. Prime Video lists Alan Ritchson as a guest star, not a series regular, and it's a brief appearance.
What happens between them?
Neagley offers Reacher her hand to shake. That's a big deal because Neagley has a lifelong aversion to being touched. The show ties it to something she saw as a child. The handshake is her choice, on her terms, and it isn't a sign she's suddenly over it.
Maria Sten, who plays Neagley, has said Reacher is the person who was "always there for her". That is the reason she picks him for that first step.
Why he isn't in the rest of the show
Neagley is built to stand on its own. The mystery and the villains are all new, and Neagley carries the story herself. One review of the finale says the season never felt like it missed him.
Do you need to have watched Reacher?
Not to follow the plot, but it helps to know who Reacher is to her. See do you need to watch Reacher before Neagley.