Forcing clique immersions through chromatic number

Building on recent work of Dvo\v{r}'ak and Yepremyan, we show that every simple graph of minimum degree $7t+7$ contains $K_t$ as an immersion and that every graph with chromatic number at least $3.54t+4$ contains $K_t$ as an immersion. We also show that every graph on $n$ vertices with no stable set of size three contains $K_{2\lfloor n\mathrm{/}5\rfloor }$ as an immersion.