Learn Swedish: Piraten lär plundra fartyget där kungen bor. - The pirate is likely to plunder the ship where the king lives.

You would attach the -s to the very end of the entire descriptive phrase, right onto the verb bor. You would say fartyget där kungen bors skatt. While this sounds a bit clunky, it is grammatically correct and very common in everyday spoken Swedish. In formal writing, you would usually rephrase it as skatten på fartyget där kungen bor.

Why does lär mean 'is likely to' here instead of 'learns'?

When lär is followed directly by a verb in the infinitive (like plundra without att), it acts as a modal verb meaning 'is likely to', 'will probably', or 'is said to'. If you wanted to say the pirate 'learns to' plunder, you would need the reflexive pronoun and att: Piraten lär sig att plundra.

Since där means 'where', could I also use som here, like fartyget som kungen bor i?

Yes, exactly! Fartyget där kungen bor (the ship where the king lives) and fartyget som kungen bor i (the ship that the king lives in) mean the exact same thing. At a B2 level, it is great to practice using both relative adverbs like där and relative pronouns with placed prepositions like som ... i.

Is fartyget the best word for 'ship' here, or could I use skeppet?