Use a multi stage process
1) clean the leather
Use a damp rag to sponge off dead bugs, coffee, red wine ...etc
A little "Dawn" or equivalent detergent can assist
Then deep clean with a good quality Saddle Soap .. this will remove dirt deep in the leather grain
The more time you spend on this the better the result.
2) condition the leather
Use a good quality Leather Conditioner and slather it on, pay extra attention to any areas of stitching (seams, Zippers and straps)
It helps to warm the jacket up to body temperature using the sun, a hair dryer (on low) or a warm room.
Avoid direct heat or putting it too close to a heater or fire
Leather conditioner will be absorbed into leather .. leave in the warm room
repeat until no more can be absorbed
Wipe off any remainder with a soft lint free rag.
Any good quality Beeswax, Linseed oil, Neatsfoot Oil type product (SnowSeal, Boot Grease, Limmers, Obenaufs etc.)
Warm the jacket using a warm room or a hair dryer, warm the product by placing the jar in warm water or leave it in the sun or next to a heat source.
Slather on the product using your bare hands so your body warmth melts the product into the seams (Be generous)
Use the hairdryer on low to push the product into the leather
concentrate on seams, zippers and straps as well as the front of the jacket and arms.
Leave the jacket to absorb in all the product in a warm room.
Repeat until no more product can go into the jacket.
Wipe off remainder
Buff with a soft cloth and a horsehair brush to bring out the natural shine.
Australian "RM Williams" Saddle Soap and Leather Conditioner
I also use Snow Seal and/or my own version made from Beeswax, raw Linseed Oil and Gum Turpentine.
Avoid Dubbin .... Most of the products marked Dubbin are petroleum based and not the original 'Natural" recipe.
The solvents in modern dubbin can dissolve any adhesives in jackets or boots causing the leather to delaminate.
Avoid using Animal based oils (Neatsfoot etc) unless you are very familiar with them
Overuse will soften the leather fibers causing the jacket to collapse on itself and lose shape
It can also cause stitching to pull out at stress points.
This has worked for me YMMV.
My leathers and gloves are 40 years old and still providing warmth, waterproofness and comfort.