Use glycerine saddle soap to clean your leather - then re nourish with a leather dressing. Ko-cho-line is very good as is the Sedgewicks dressing.
If you warm the dressing up before rubbing in this will help.
I wouldn't advise wrapping any leather up in clingfilm as it should be allowed to breathe - if you can , get a grain sack ( not plastic ) from a feed store and put your harness in there. I keep mine in an old suitcase - not only does it keep it in good condition but I don't have to worry about any rodents eating it whilst I'm not using it, and it keeps most of the moisture out so mine doesn't go mouldy.