Reduction for the proof that COMBI $:= \{\langle G,k \rangle | G$ has Clique $\geq k$ or Independent Set $\geq k\}$ is NP complete
Let $\langle G=(V,E), k \rangle$ be an instance of CLIQUE with $k \ge 1$, and let $n=|V|$.
Let $S$ be a new set of $n$ additional vertices.
Construct a new graph $G'=(V', E')$ with $V' = V \cup S$ and $E=E' \cup (S \times (E \cup S))$.
Now consider an instance $\langle G', n+k \rangle$ of your problem.
If $G$ has a clique of size $k$ containing the vertices in $C \subseteq V$ then $G'$ has at least one clique of size at least $n+k$. Pick, e.g., the clique induced by $C \cup S$.
If $G'$ has a clique or an independent set of size $n+k$ then let $C$ be the set of vertices that induce such a clique or independent set set.
Since $C \cap S \neq \emptyset$ and $|C| \ge 2$, $C$ cannot be an independent set and therefore it is a clique. Then $C' = C \setminus S$ is a clique of size at least $n+k-n=k$ that is also a subgraph of $G$.