We consider that the "new moon" is the beginning of the cycle, so the next is "first quarter".
New moon.
The phase of the moon that comes after the third quarter is the waning crescent. It appears as a small sliver of light on the left side of the moon.
the Waning crecent moon
Waning gibbous, then last quarter.
Waning crescent
Waxing Gibbous Moon!!!
The full moon phase comes after the first quarter moon. The full moon appears as a complete circle in the sky, with the sun illuminating the entire side facing Earth.
The First Quarter moon
Last quarter moon comes after the full moon
The next moon phase after the third quarter moon is the waning crescent moon. It is characterized by a decreasing illuminated portion of the moon visible from Earth.
Last or third quarter.
No; it comes after. In order, the phases are: New Moon, waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, third (or last) quarter, then the waning crescent.