If it's really bad, Dr. Jackson's Hide Renewal. My mom uses that religiously for stubborn tack.
Regular saddle soap and than Ko Cho Line- best stuff EVER! A little bit goes a long way.
Soak it in a bucket of neatsfoot oil! Beware it may darken the leather. But brought my old bridle back to life and looks new now!!!
Leather CPR is amazing. It can bring really moldy leather back from the edge.
I would it up really good with glycerin soap or a regular leather cleaner. I would then use a really good conditioner on it to hydrate the bridal so it's not so dry and hard to bend. Do this for about a week, maybe less, and it should come back to life!
Hope this helps!
Just clean it good! I personally would avoid oils because in my past experiences I have had the leather break afterwards. I would just wipe it down and maybe scrub with leather cleaner and maybe add a touch of conditioner (not oil)