The left tail light on my trailer doesnt work.the stop and turn signal works . is there a fuse for it? i have 2011 gmc sierra 1500

There is a tail lights fuse for the truck, but not for the trailer.
First, check that your left tail light on the truck is working, if not fix the problem (new bulb, bad contact, fuse).
Then the obvious suggestions regarding the trailer are: Check the tail light portion of the bulb to be sure it is not blown. If good (best to put in new one to be sure), then check the wiring from the front of the trailer all of the way to the non working bulb, including every connection and at any place it is secured to the trailer frame. If all is good with the trailer circuit and bulb, then check the truck's trailer connector, including any adapters. If by chance the truck is wired with a flat 4 wire harness the problem may be solved (but usually the blinkers are the problem). Modern trucks require a 5 wire harness which self adapts to the standard 4 wire trailer circuit. Check for dc power (12 volts) from the truck's female connector. One wire will be ground, others will be taillights (turn on headlights), brake lights (have someone press brake pedal), and blinkers (turn on switch and blinkers).