Recurence for Insertion Sort
Actually, it is pretty simple. Let $T_n$ be the running time for a given array $A[1,...,n]$. As you've mentioned, we first sort $A[1,...,n - 1]$ whose running time is $T_{n-1}$ (since it has $n-1$ elements) and then we inset $A[n]$ to the sorted list, whose running time is $O(n)$ (since we need iterate over the whole array at the worst case).

Therefore, $T_n = T_{n-1} + O(n)$. And do not forget about the base case which is $T_1 = O(1)$.