I had a lot of respect for Henry Gregson-Williams, who did the score for the Walden adaptation of The Lion, The Witch, and the Wardrobe and Prince Caspian. If Netflix wants to bring him back, I'd be fine with it. I also thought of Hans Zimmer, who a big time composer, who did score The Dark Knight trilogy, The Lion King, Inception, Gladiator.. the list just goes on. Or even Howard Shore, who did the score for the Lord of the Rings trilogy and the Hobbit trilogy. Now there's someone who could do the score for both Tolkien and CS Lewi's universes.

My answer for this question is always Bear McCreary. Most of his work is TV, but he's also done movies and video games in a lot of different genres. He's incredibly versatile and each soundtrack he composes is unique. Compare his work on Black Sails, Outlander, and Battlestar Galactica to get a good idea of his range.

And for a slightly out of left field suggestion, I'm a big fan of Austin Wintory's work. He's mostly done video games, but the Journey soundtrack is magical.

I would love to see Patrick Doyle or Brian Tyler, who did Thor and Thor: The Dark World respectively. I felt like their scores did a great job of making you feel both the power and the beauty of the fantasy environment they were working within. I’d also be totally onboard with the Bear McCreary suggestion, it feels like every time there’s something that makes me really emotional it turns out to have been him.

A slightly off-the-beaten-path composer that I personally think could do a really good job is John Paesano.

He scored the Maze Runner films, as well as Netflix's Daredevil series.  He's able to do the sweeping and epic types of pieces, as well as ethereal and otherworldly, both of which are things that Narnia's soundtrack will need. 

Here's one of my favourite pieces by him.