How to add new colors to tailwind-css and keep the original ones?

You can simply concatinate them using "Array/Object spread operator" (...) and gather them all in a colors variable.

// tailwind.config.js
const { colors: defaultColors } = require('tailwindcss/defaultTheme')

const colors = {
    ...defaultColors,
    ...{
        "custom-yellow": {
            "500": "#EDAE0A",
        },
    },
}

module.exports = {
    "theme": {
        "colors": colors,
    }
};

Add your custom color values to theme > extend > colors section in tailwind.config.js

//tailwind.config.js
  module.exports = {
    theme: {
      extend: {
        colors: {
          'custom-yellow':'#BAA333',
        }
      },
    },  
  }