Wingtip landing light lenses are hazed - what can I do to make them clear again?
The hazing is a collection of very small scratches on the acrylic, and the way to remove them is to actually remove a thin layer of the acrylic - the trick is to make sure you use something that won't damage any of the paint/metal around the cover.

A mild acrylic polish is your best bet, although any mild abrasive will work (including non-"sensitive" toothpaste and a paper towel... although it might take a while!). There are plenty of "Perspex cleaner" style products for a reasonable price to do it.

Use a small amount (multiple small applications are better for controlling the spread) and try to use a thicker "paste" type of abrasive rather than a runnier one, for the same reason. Apply a small amount and some fairly firm pressure with a cloth, as per the instructions of the cleaner, removing any excess regularly.

If you think there are deeper scratches than just a very fine "hazing" on the lens, you can use a fine sandpaper (eg 1600 grit) to sand the acrylic first before using the polish