If the right one works,it might be a bad bulb or a bad ground.
Replace the turn signal flasher relay.
You may have a "ground loop" problem on the left turn signal. Check the ground wire at the front and rear signal bulbs.
was jeep in accident and repaired? sounds like crossed or shorted wires
I suggest that you check in back by the trunk and back lights the there may be a short or the wires are lose
More than likely the Flasher Relay is bad. If the bulbs are lit but will not flash it is definitely the Relay. This can also indicate a bad bulb on one of the lights on the side that does not flash.
If you mean that the arrow inside the dash turns on and stays on then your problem is one of the left side turn signal bulbs. Test by turning on your four way (hazard) lights and observing all lights. The one that does not flash is the bulb that needs replacing.
You need to locate your flasher, usually near your fuse box; is sounds like your flasher is burnt out for that side.
You have to replace front and rear bulbs.
Turn on the RIGHT turn signal then get out of the vehicle and see which lights are flashing. Count the number of bulbs that are flashing on the back of the vehicle and on the front. Then turn on the LEFT turn signal and check again. Usually a rapid turn signal indicates that one or more bulb has failed.
When it flashes fast it means you have a burned out bulb omn that side. Check all you lights and you'll find the one that's burned out.
Short to power in the brake light circuit. Most likely, the fault is in the switch itself.
Bad turn signal flasher.