What is the religious ruling regarding someone who slanders another in their absence by gesturing, then regrets it and wishes to repent, knowing that they cannot reach the person to ask for forgiveness, and is giving charity on their behalf prescribed or an innovation?

Slandering a believer is one of the gravest sins, and one must beware of it, whether explicit or implicit, as Allah Almighty says: "And those who accuse chaste women and then do not produce four witnesses - lash them with eighty lashes and never accept their testimony thereafter. And those are the defiantly disobedient."

You have done well by repenting and feeling remorse. You must seek forgiveness from the one you slandered. If you cannot reach them, then you must increase good deeds, make abundant supplications and ask for forgiveness for them, and speak well of them in gatherings.