in a graph G= (V,E), finding a clique of size |V|- d where d is some constant
The brute force algorithm would check all vertex subsets of size $n-d$, where $|V|=n$. There are $$\binom{n}{n-d} = \binom{n}{d}=\frac{n(n-1)\dots (n-d+1)}{d!}$$ different subsets. This quantity is $\mathcal{O}(n^d)$ and since $d$ is constant this problem is in $P$.

You are asking 


  Is the question above still NP? 


Even though the problem is in $P$, this problem is still in $NP$ since $P \subseteq NP$, however, unlike $k$-clique problem this problem  may not be NP-complete.