I was hoping to have a PC kill a NPC. in essence I was using the dark brotherhood start quest from skyrim for inspiration. so you could just call it a contract killing and resolve it like a combat. but I didn't know if it would relate to a specific skill check or mechanic. also at the moment we only have the starter set and don't have all feats, skills or classes available to us. although we are looking to purchace the core book after our enjoyment of our first few games.
It all depends on how the assassin wants to kill the target. If they're sleeping coup de grace is good. Using a poison is another option. My favorite missions from the dark brotherhood were when you could make it look like an accident. (Weakening supports on a balcony) But in the end it really should be up to the playerto decide how they approach the problem. Your job is to give them a problem to solve and maybe hints on how it can be solved, then taking their solution and interpreting proper skills/abilities to use for it.
Ex. Disguise to make yourself look unassuming
Stealth to follow him from the pub.
Bluff to lure him into a dark alley.
Silence spell to muffle any sound of a struggle.