In my opinion, I see Clover deciding to give up their SOUL at the end of True Pacifist as them acknowledging that there's nothing that they can do for the other Fallen Children. They're all dead, so even if they marched up to Asgore right then and there and succeeded in killing him and "avenging the Fallen Children," that's.... Not going to change the outcome at all. They're still dead. Nothing they can do will change that fact.
What Clover did come to realize over their journey is that monsterkind is suffering imprisoned Underground and their SOUL can at least right some of the wrongs inflicted against monsterkind by humans by bringing them closer to freedom. And by giving their SOUL to Ceroba, they give her the chance to redeem herself from someone who was trying to kill them for their SOUL to fulfill her husband's dreams at arming monsterkind for combat, to someone who can bring hope to monsterkind with their SOUL in another way. It's restorative justice.
By killing Ceroba at the end of Pacifist, what then happens is that Clover acknowledges that some people have to die in order for justice to be achieved. Punitive justice/death of the wrongdoer is still an acceptable outcome. Hence why they try to fight and kill Asgore after they see the Fallen Children's SOULs.
So yeah. Personally I can't see Clover trying to restart their mission should they decide to live with their friends. They still deeply resent Asgore for killing the kids, but I can't see them marching up to him and killing him to try to resolve things because it won't fix anything. And also, their friends are committing treason by hiding them and raising them in these Clover Lives AUs, they're not going to jeopardize their friends' safety by exposing themself.
BUT! I also think that when Frisk falls into the Underground, and now there's a LIVING human child walking around, that would definitely change up what Clover decides to do. It would certainly be a kick in the rear for them.
