There are a couple of things that can be done here.... The right way and the wrong way.. Both ways will work OKay:-)
The best way to fix your problem is to go to a reliable antenna/electronics supplier. Ham radio equip. supplier or even on ebay and find a antenna lead extender/extension. It will be a length of car antenna lead that will plug into the lead coming off the existing antenna lead. They come in variuos lengths for what ever you need. However this way will require the removal of the old one that goes to the radio and the routing of the new length from the antenna to the radio... No big deal really. Thats the best way...
The wrong way to do it is to splice the old to the new. The cables are made of two conductors. One is the outside conductor, and is the braided wire usually braided steel wire. This wire is called the sheild wire and it is to keep unwanted signals from entering into the signal on the center solid copper conductor, called the signal wire. Strip back the rubber coating, using a razor blade carefully slit the braided wire about and inch or so and undo the braid enough so you can access the plastic covering of the center copper wire. Do this to both ends that you are going to marry together. CAREFULLY strip back the center plastic cover until you have enogh copper center conductor showing to make a hot soilder connection between the two center conductors of each lead. With that connection done wrap the connection fully with electrical tape. Now pull the braided sections towards the the connection point and rebraid the best you can the outer conductors together. Then fully tape this connection. Keep in mind that the two conductors cannot touch together-- that would create a signal short and the antenna signal will not get to the radio. With this complete do your best to hide the cob-job connection:-) You wouldn't want anyone to see this abortion... It is ugly but will work just fine unless you live near the artic circle were there are no stations for several hundred miles. If this does not work for you see to solution#1.