Say we two fields $K \subset L$, and an automorphism $\sigma : L \to L$ fixing $K$. I have an $L$-vector space $V$, and a map $t : V \to V$ with $t(lv) = \sigma(l) \, t(v)$ for $l \in L$ and $v \in V$.
It's a $K$-linear map, but not $L$-linear. Is there a name for such a thing?
Assuming that your $t$ preserves sums too, it is a $\sigma$-semilinear transformation.
(In the particular case that $L=\mathbb C$ and $\sigma$ is complex conjugation it is "conjugate linear" or "antilinear").