Successor

$666 \text{ in base 7 is } 6 + 6 \cdot 7 + 6 \cdot 7^2 = 342 \text{ in base 10 } \Rightarrow$ $\text{ next number is } 343 = 7^3 \text{ in base 10 } = 1000 \text{ in base 7}$

Add $666 + 1$ like usual except you carry over when you get to 7 instead if when you get to 10.

You will get $\boxed {1000}$ .