First, carefully remove the old cork from the tenon. This should be scraped off without damaging the tenon itself. Remove the glue residue with an appropriate solvent. Keep alcohol away from plastic clarinets. Alcohol will cause plastic clarinet bodies to crack and craze. A safe solvent to use is Mineral Spirits. It will remove most contact -type cements.
Once the tenon is cleaned, you need to measure the width of the slot in the tenon so you can cut your cork. This done, put a coat of contact cement on the tenon and set it aside.
We need to make the cork with a slight bevel to fit into the cork slot tightly. The best way to do this is to use a metal ruler as a straightedge and cut off a small amount of the sheet cork by placing your cork knife or single edged razor blade at an angle, (down and to the left), and drawing the blade the full width of the cork. This will give you one beveled edge to work from. Now turn the cork over so the beveled edge is facing up and on the right hand side. Measuring from the inside/top edge of the bevel, mark the width of your cork slot at both the top and bottom of the cork. I like to use the back side of my cork knife to press a mark into the cork, but any thin mark will do You should now have the bevel on the right, and 2 marks on the cork to the left. Place your ruler on the marks, and cut the cork so as to cut the second beveled edge, again down and to the left. You should now have a strip of cork which the narrower bottom side will fit your tenon nicely. Remember, the beveled edge goes down into the slot. The left over material on top will be removed shortly.
The final preparatory cut is to cut the bevel for the lap joint. With the beveled side of your tenon cork facing up and horizontally placed in front of you, cut a bevel on the right hand end of the cork; again down and to the left. This bevel will be used to form a lap joint that will be smooth and strong. With the cork still in this position, horizontal, with end-lap on the right, apply an even, thin coat of glue to the cork. Now turn the cork over, and apply glue to the lap joint bevel on the other side of the cork. Let the glue dry.
Now we must install the cork onto the instrument. What we want to accomplish is to have the lap joint wind up on the back side of the instrument, i.e., the side of the instrument opposite the label.
Holding the instrument in front of you with the glued tenon up and the side of the instrument with the label facing you, place the cork onto the slot so that the lap-joint bevel is on your left and hanging over the side about 1 inch.. Apply the cork with such light pressure that the cork may even fall off under its own weight. Do not press the cork down into the slot yet. Now is the time to check that the cork is straight in the slot and perpendicular to the bore of the instrument.
When you are certain that the cork is in the correct place, press the cork firmly into the slot. Start at the middle, and work to the left, towards the lap joint. Work a little at a time and keep the cork straight in the slot. When you reach the lap joint, wipe off your thumb to remove any oil, and carefully press the bevel firmly into the slot. Now go back to the middle of the cork strip again and work to the right until you come to the lap. Press the cork into the lap bevel tightly so as to avoid any gaps under the cork. Cut the leftover cork strip even with the lap joint.
Now comes the final shaping. Place the tenon against a bench peg, or on a drumstick or dowel rod held in a vise and covered with a loose piece of cloth. Note: Make certain that the cloth does not crawl up into the bore of the instrument. Keep some in sight at all times so as not to get it stuck in the bore. Using a ½ inch wide strip of 220 grit emery cloth about 6 inches long, , sand the lap joint on the cork smooth. To cut the cork down on the edges, care must be taken so as not to sand any of the tenon itself. Do not let the abrasive touch the tenon! Bevel or round the leading edge of the tenon cork more than the inside edge. The bevel will help start the tenon into the socket. You need to remove enough material from the cork so the joint goes about halfway together without grease. Once you have reached this point, grease or wax the joint. Try the fit. It should be tight and firm, without rocking. If the cork is on correctly and the joint wobbles, then the tenon needs professional care. Have it sleeved, replaced or somehow repaired by a tech that you trust. It is possible to cork the tenons fully to remove the wobble, but this can be tricky. Remember, new tenon corks like cork grease. Be gentle.