My first interpretation of the question was about listening to music, so I'll give my opinion on that. I don't know if 'skill' is the right word, but it's certainly something which others seem to have a kind of instinct or 'talent' for, and a knowledge of what it is they're listening to. The American composer Aaron Copland wrote a book called 'What To Listen For In Music', and it's fascinating. I still don't have anywhere near the level of 'understanding' of music that he and other musicians/composers/musicologists have, but it did make me realise that I'm not 'hearing' around 90% of what's going on in, say, a Beethoven string quartet.
A similar thing seems to be the case in cinema. I'm constantly amazed how certain reviewers or critics can notice details in films which I simply don't catch. I'm not talking about improbable theories about 'what the film-maker meant by this or that', I mean actual details on screen (I recently watched an analysis video of The Big Lebowski, and the guy was highlighting all the 'subliminal' castration imagery used in the paintings behind Maude when she meets Jeff Lebowski for the first time. I've seen that film maybe 50 times, never even paid attention to that stuff before).
So yeah...I'd say we can roughly call listening a skill, and it's not one I have, though I try to develop it by learning about the things I'm listening to.
(If the question is about listening to people, then yes, no doubt that's a skill requiring empathy, awareness, experience, self-perception etc).