Learn French: Il s'agit du successeur ; je ne m'oppose pas à lui. - This is about the successor; I am not opposing him.

Because s'opposer is a reflexive verb. French grammar doesn't allow you to put an indirect object pronoun (like lui or leur) right before a verb that already has a reflexive pronoun (like me, te, or se). To avoid this clash, reflexive verbs followed by à must keep the preposition and use a stressed pronoun (like lui, elle, or eux) after the verb when referring to a person.

What if I were opposing a new law instead of a person? Would I still use à lui for "it"?

No, the à + stressed pronoun structure is only for people. If you are opposing a thing, an idea, or a project, you replace à + [thing] with the pronoun y, placing it before the verb. To say "I am not opposing it" (the law), you would say Je ne m'y oppose pas.

Why does the sentence use Il s'agit du to say "This is about the"?

Il s'agit de is a very common fixed expression meaning "it is about", "it's a question of", or "it concerns". It is always impersonal, meaning the il doesn't mean "he", but rather the abstract "it" (just like in il pleut). Because successeur is a masculine singular noun, the preposition de contracts with the article le to become du.