Ghee is one of the easiest things in the kitchen to store, as long as you remember one rule: keep water out.
The dry spoon rule
A wet or used spoon brings water and food bits into the jar, and that is what makes ghee smell stale. Keep a dedicated dry spoon, or pour a little into a small bowl for daily use.
Winter
In the cold, ghee sets firm and grainy. To soften it, stand the closed jar in a bowl of warm water for a few minutes. Avoid heating the jar directly on the stove.
Summer
In hot weather ghee may turn partly or fully liquid. That is fine. Keep it away from the stove and sunny windowsills. In a very hot kitchen a cool cupboard is better than the counter.
Monsoon
Humidity is the real enemy in the rains. Close the lid tightly every time and wipe the rim so moisture does not collect under the cap.
Does it need the fridge?
No. The fridge makes it hard to scoop. If you do refrigerate it, take out only what you need so the rest does not keep warming and cooling.
And always go by the best-before date on the label.