Especially if the item came from a secondhand store or a friend, regardless of the fiber content of the item, you should make sure there are no signs that the item is infested. It is possible that stray caterpillars could be attached to the clothing and end up hatching in your closet. In the United States, most infestations come from webbing clothes moths, but you should still inspect for both.  Look for patches of silk webbing and feeding tube which webbing clothes moths leave behind. Casemaking moths' cases will change to match the color of the clothing they're eating. For this reason, you should always look for numerous, suspicious small holes as this your best warning sign for an infestation. Frequently clean your closet from top to bottom; moths like to live in places where it's dark and they're undisturbed. Move things around: move your clothes out, wipe things down with detergent-soaked clothes, and vacuum the floors and drawers. You might think that your clothes, particularly those made out of cotton and manmade fibers, will be okay as long as your wool is stored separately. But moths like to eat the tiny detritus left behind from human skin, like sweat, as well as food particles. Make sure your clothes have always been washed before they return to your closet space. You can use vacuum sealing, ziplock bags, or even plastic containers with airtight lids to store your wool garments when you're not using them. This is particularly helpful in the spring and summer months. You can also line these spaces with anti-moth paper, cedar, or even mothballs to make them extra secure. Most if not all of these items should be available from Amazon, Bed Bath & Beyond, Target, or Walmart.  Be careful: storing clothes in an airtight container can only keep new infestations from happening; if your clothing already has eggs on it, they'll hatch and eat the clothes anyway. Be sure you've properly cleaned your clothing first. Make sure the containers are also dry, as are your clothes, to prevent mold. The strong smell of cedar helps to camouflage your clothes from moths. You can invest in cedar furniture to store clothing, but if that's too expensive, cedarwood hangers, cedarwood blocks, and even oil diffusers that use cedarwood's aromatic oils are affordable solutions. JCPenney, Bed Bath & Beyond, and Amazon will all carry them.  There has been some limited evidence suggesting that Eastern Red Cedar (actually a juniper) contains an aromatic oil that, over time and with a sufficient enough concentration, will kill small moth larvae. However, a closet would provide too much air circulation to be lethal to larvae, and would probably only serve as a deterrent for the adult moths. Eastern Red cedar is only effective for a few years. After a while, the aromatic oil contained within the wood will evaporate, rendering it ineffective in a fight against moths. It's long been thought that certain herbs and food products could protect your clothes from moths. The theory is that, for the same reason that cedar is effective (a very powerful odor), moths can be similarly kept at bay by other strong odors. In a recent experiment, researchers found that cinnamon, cloves, and lavender were all effective at keep moths from eating clothing. You can make sachets or put out a bowl of scented oil in your closet.  Some aromatic herbs, like bay leaves, eucalyptus, lemon peel, and mint proved to be ineffective in the experiment, so be careful about which herbs you use. Beware that some of these scents are very difficult to get out of clothing, in case you or loved ones dislike or have any allergies to these plants. Whether you're trying to prevent an infestation from occurring for the first time, or trying to prevent one from recurring, you should check your clothing throughout the year. Look for signs of an infestation, which generally amount to suspicious and multiple holes in your clothing.  Although this is particularly important during the months your clothes are not stored in plastic containers, it's also important to check at least once after you've stored them: adults live for about 75 to 80 days, and eggs hatch into larvae after 4-10 days. If moth eggs managed to make their way into the storage item and go unchecked, you may come back to ruined clothing months too late.  Moving and shuffling your clothes around during this process is actually very helpful because moths do not like to lay their eggs in places that are frequently disturbed.
Inspect any recently purchased items. Keep your closet area clean. Keep your clothing clean. Store clothing in airtight containers. Use cedar. Use natural, food-based repellents. Periodically check your clothing.