Multicoloured Clique — given a graph whose vertices are properly coloured with $k$ colours, is there a clique with one vertex of each colour? — is W[1]-complete under fpt-reductions, parameterized by $k$ [CFK+15, Theorem 13.7]. It is the usual starting point of W[1]-hardness proofs.

• $p$-Clique $\le$ Multicoloured Clique. Take $k$ copies of the vertex set, copy $c$ coloured $c$, and join $(c, u)$ and $(c', v)$ when $c \ne c'$ and $uv$ is an edge. A multicoloured clique picks $k$ distinct pairwise adjacent vertices, and conversely.
• Multicoloured Clique $\le$ $p$-Clique. Forget the colours: adjacent vertices have different colours, so a clique of $k$ vertices in a $k$-coloured graph has one vertex of each colour.