Gently wet rub with 800grit wet and dry paper to a nice even matt finish, this will remove a couple of microns (or less) of the surface, which is mostly, all "oxidised" material. Being an oxide it is very “hard” and to remove it by simply trying to taking it off with a cut and polishing compound would take “forever”. After the wet and dry, then cut and polish with a lambs wool buff at slow revolutions using a coarse cut and polish compound. This will bring the surface colour back up to “as new” and the actual polished surface will be better than new.
When the surface “oxidises” it is doing just what it was designed to do – protect the resin in the laminate from UV breakdown. UV light will break down ALL resins regardless of whichever they are, and the gel coat is there to primarily protect the resin in the fibreglass laminate from this UV breakdown. Unlike exposed resin in a fibreglass laminate where the resin will quite quickly “breakdown” and just crumble and fall away with extended, unprotected UV exposure, gel coat will oxidise on the surface and that oxide stays there and will then, itself help in the protection from UV breakdown.
If you want to keep the high gloss, full colour surface without the “milky/chalky” appearances caused by the gradual oxidation returning, then, after the surface has been restored, spray paint it with a coat of clear automotive lacquer or a clear, two pack (good) polyurethane paint. The surface finish, colour, and gloss, will then last for many many years even when left continuously out in full sun exposure.