You need to take care of your vegetable tannned leathers as they loose their content of grease and oils with time. I give recommendations for your new items as well as how to preserve them for the long term.
To soften and feed leather
New leather is a bit stiff, you can soften the leather with your hands, working it delicately. Do not fold the leather sharply when it is still stiff. The usage of the item will do the rest to obtain a supple leather.
About 3-4 times per year or when needed, use a nourishing cream to feed the leather. I recommend a natural cream like the Sedgwick's natural leathercare, Jeffries natural leathercare or Stubben Hamanol available in tack shop.
Unbuckle all pieces and wipe tack clean with a damp sponge or cloth and leave to dry naturally away from a heat source. Apply natural leathercare sparingly and evenly to both the grain (top) and the flesh (back) of the leather, make circles and let the cream heat and penetrate the leather. When dry to touch, buff with a dry cloth.
To wash and maintain the leather
Only use a damp sponge to remove the dust, sweat, etc.... Let dry naturally away from a heat source. You can use product like lexol PH to clean leather. Glycerine saddle soap bar can be used on the side and grain of leather to clean, maintain pliability, give a nice polished edge and show finish. Be aware that glycerin soap tend to dull colors, especially blacks. You may preffer a light beewax cream for frequent conditionning after washing leather instead of glycerin. If your black leather is fading, i recommend Fiebing black saddle soap paste.
If the leather is wet
Do not hang over or close from a source of heat to dry, it will harden the leather. Let dry at room temperature, use a nourishing cream just before it is completely dry.
To store the leather
For long term strorage, unbuckle pieces if they are of solid brass, as they produce green oxide and place the leather piece in a wool, cotton or linen bag in a temperate room. Cream every year or when needed.