Here's how it's usually used:
* Sports: A player might "put a full kit on" before a game, meaning they put on their full uniform.
* Military: Soldiers might "put a full kit on" for a mission, meaning they wear their complete combat gear.
* Work: Someone might "put a full kit on" for a special event at work, meaning they wear a formal suit or uniform.
The phrase "full kit" emphasizes the completeness of the attire, implying that every piece of the necessary gear or uniform is worn.