Used as a noun or prefix to indicate a great length in space or time. Often appears in literary or formal contexts, and in compounds like 長きにわたる (over a long period/distance).
We are grateful for your long-standing support.
After a long journey, he finally arrived at his hometown.
Alternate kanji form, less common and may carry a nuance of 'eternal' or 'perpetual' in some contexts.
Derived from the classical Japanese attributive form of the adjective 長し (ながし), which corresponds to modern 長い (ながい). The form 長き is now used as a noun or prefix in modern Japanese.