What Should I Do About HR Staffer Who’s Discussing Pay?

If He/She has been your trustworthy person at some time then it is good to counsel. But since you have already pointed this out in a meet then i think best practise is to relieve.You cannot take chances with such resources in HR dept.
Regards.
Manpreet

Rashid,
You know more about him then all of us. You will know yourself if he is the kind to respect constructive feedback or not.
As I see it, you have two options:
1: Fire him/her immediatly. Make an example, because if HR is discussing salaries then trust factor of the whole company is under question. you may never be able to reprimand another employee for doing the same mistake.
2: On the other hand, if you feel he is good at work and is doing it more out of a habit to gossip and chit-chat than with any malice in heart for the company; then move him to another department where his/her work can be appreciated and he/she does not get a chance to gossip thus. Make sure he knows why this move is being made.
Regards,
Kavitha

The person who is leaking the salary related info must know that, he is doing what he is not supposed to. Now the point is- Is he doing this to get any favor from the people with whom he is sharing the info or he is under pressure (of some kind) from that particular group of people.
Try to find out may be that person is betrayed by someone or group of people.
We had the same situation. She used to share salary related matter with the group of people who belong to her community. Even after given warnings she couldn’t stop sue to the pressure from same set of people threatening her not to include in the group if she doesn’t share info with them. Finally we had to remove her from that position.