Depending on the value and the age of the antenna, it might be better to replace it. Anytime you cut a length of coax and insert connectors you stand to degrade the signal. Depending on what frequencies you are listening to the loss could be substantial.
Solder the the center conductor and then fill the gap by wrapping with tape to the diameter of the center insulation. Cut strips of aluminum foil the correct width of the peeled back braid section and wrap around the taped area. Pull the braid up around the foil and solder together in several areas. Tape the enitire area.
Did this once on a CB cable while out in the middle of nowhere. Had a 12v solder iron and used the foil from gum wrappers. It worked well for a long time.