Cautionary note: Restoring or altering a cover can affect the value. Many collectors would rather have a cover in its existing condition than have one in which has had modifications. Some collectors feel doing minor restorations to their covers is acceptable and repairing tears is within acceptable limits; others do not. No matter how you feel about the restoration of stamps or covers one thing remains the same; if you make any restorations to any item you should document them and offer full disclosure to any future buyers of that item.
Remember that any restoration should be archival safe, and it is therefore very important that any product used to repair a tear be safe and harmless to the cover. This is not as easy as it sounds as the vast majority of tape or other adhesive that might be used to repair a tear will not meet the “archival safe” standard.
That being said, there are some products available which can be used to *temporarily* mend cover tears. These include stamp hinges, tissue mending tape (sometimes called “library” tape), and others. I suggest visiting a website online where archival safe tape and other related archival-safe products can be bought. The product I’ve used for years (since I do very little of this type of work) is “Transparent Mending Tissue” by Linco, Inc. Suppliers for this tape can be found using a online search engine. It is inexpensive and unless you do a lot of repair work, will last a long time. So assuming you are using a “safe” product, we will proceed.
First, flatten both sides in the torn area. Then join them together, either by holding the sides together (being careful that the tear is closed fully) or even by tacking the front of the tear together enough so that the tear is fully and accurately closed.
Keep in mind that you want to repair tears by taping the BACK of the tear so the tape is out of sight. While tears can certainly be closed on the front of the cover, it will not be aesthetically very pleasing. Then apply the tape or hinge to the back of the tear, being sure to apply a lot of downward pressure to join the sides together fully. That’s it!
When using peelable stamp hinges, they can be cut into narrower strips than the normal size of a hinge. The less tape or hinge used to mend tears, the better. Mending/closing tears can greatly improve the appearance of the cover, thus also possibly the value. Stamp tears can also be closed using this method. For stamps, tiny thin strips of the gummed tape or hinge are used.