You need the part number of the LED and its manufacturer's name so you can look up the datasheet that will have ALL the details of the LED:
1) The absolute maximum allowed continuous current.
2) The recommended current for a certain brightness.
3) The range of forward voltage at various currents.
Buy from a good electronics parts supplier, not from a shopkeeper who is called "e-bay" and knows nothing about the products he sells.
Most ordinary LEDs are only 5mm in diameter and operate brightly at 20mA. Your LED is much larger so its recommended operating current might be higher.
The color of an LED roughly determines its forward voltage. A red LED is about 1.9V and a white or blue LED is about 3.4V.
If you have a 1.9V red LED and a 12VDC power supply then the current in the 1k resistor and LED is (12V - 1.9V)/1k= 10.1mA.
Maybe your large LED has two or three LEDs in series inside. Then its forward voltage is much higher than one LED.