Whether an employee is from HR or any other department or function, the issue needs to be addressed in the same manner. You cannot and should not terminate an employee just because he/she is reminding you about something daily.
The reason why the employee is coming daily and reminding is that she did not receive any satisfactory and firm answer from the management. Here, the management is behaving in a very defensive manner. Once they are decisive and assertive and give a firm reply to the employee, she will not come again to remind.
The employee is not at fault for expecting more salary, and reminding about it is not a crime or misconduct. There is no justification to take very extreme and harsh steps like termination.
Addressing Salary Concerns
Hello friends, those who shouted at me, please note the employee is coming daily and asking Kavita to increase salary. What nonsense is this? Just because the employee is HR, you need not be soft with him/her. HR should understand their salary and worth, and not come daily to remind about an increase. What will you do if someone comes to you daily and reminds you to increase salary? Come on, people, speak sense! Just because the employee is HR does not mean you should not consider him/her. Anyone who comes daily, complains, cribs, and spreads negativity needs to be terminated immediately.