How to get rid of musty smell?

Ole Hickory said:

Repeat after me-
NEVER EVER WASH OR LAUNDER A SPORTCOAT OR SUIT.
I've seen the above garments after being hand & delicately laundered.
It's guaranteed ruin the interlinings & destroy the finish on the fabric.
You may simply need to send the garment to the landfill & avoid storing garments similarly in the future.

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I'll spare myself from repeating your admonition as I agree with it completely. I suppose my "long-term storage" comment was a bit misleading as the coat actually spent its entire life (perhaps several decades) on a rack prior to my acquiring it unworn, but for practical purposes it could as easily have been in a closet. After speaking with the local dry cleaner I'm not going to take any action for now as the issue isn't significant enough to risk damage to the coat.

paxonus said:

I have had very good success with activated charcoal. Comes in different formats and is made just for this purpose. Put it in a bag with the garment and seal it for a few days.

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Is it necessary for the activated charcoal to make contact with the garment? If not, can it simply be placed in the bottom of a garment bag while the coat hangs inside?

paxonus said:

No. It can go in the bottom of the gament bag.

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Perfect, I'll try this. Thanks!

poppies said:

I had a thrifted jacket that defied all attempts at mustiness removal. Several dry-cleanings didn't do the trick. What did, however, with perfect results, was to fill a spray bottle with cheap vodka, spray down the jacket to just before dripping saturation, then hang it to dry in the sun.

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The garment in question is an old-stock Oakloom cashmere from O'Connell's. I'm a bit leery of applying anything to the coat directly as it's irreplaceable, assuming you're serious of course.