I would look at the REAR signal light on the same side of the car. It is probably not blinking at all and the bulb needs to be replaced.
The new bulb is already burned out, not seated properly in its socket, or you replaced the wrong one. Get out and look at the signal lights while they are blinking fast. Either the front or rear light is not blinking at all. That is the one that needs to be replaced.
Defective flasher relay.
It has been my experience that a rapid turn signal indicates there is a burnt-out signal light bulb (either front or rear) on the side of the rapid blinking signal. If the right signal is blinking rapidly, the problem is in the signal lights for the right side (front or rear) of the vehicle. Turn the rapid signal on and step out of the vehicle to find which bulb is not lighting.
Turn on that fast blinking signal light and check to see if the front and rear signal lights are both working, chances are you have a burned out bulb. If both front and rear bulbs are flashing fast, replace the flasher relay.
One of the bulbs is burned out on the left side. The left front or rear bulb is burned out. Same problem with left side blinking rapidly and right side blinking normal speed. Both left side bulbs are lighting up, however?? Replaced both anyway and the problem still exists.
The turn signal Flasher Relay is located… Front seating area, center, under dash, mounted in front driver side of console.
A fast turn signal blinking can be caused by a bulb that is getting ready to out or a bad ground. Remove the bulbs and look for corrosion around the base and in the bulb socket.
A bulb has burnt out that is why it is blinking fast. Check the front and rear bulbs.
You have a broken spring in the steering column
Usually, a fast blinking turn signal means one of the outside turn signals (front, back and side) lights is burned out.
look in your owner's manual
It means that a light bulb is out on the side where the light solid (not blinking) it could be in the front or rear of the vehicle.