Take the word literally. Someone has vowed something.

That depends on what pleasure you are referring to. The term,"promised pleasure", doesn't really mean anything. After all, who promisies, it?

Yes, basically it means that someone has made a pledge or vow to another person that will result in something pleasurable for them. Maybe the "promised pleasure" could be a romantic candlelit dinner for two, or a bunch of flowers. But whatever it is, it will be "pleasurable" for that other person.

I think that you need to give more context. It could be a literal meaning, but it's probably something more subtle. Context is king!