  In this paper, we consider the coupling of the metric-affine bumblebee
gravity to the Abelian gauge field and obtain the effective model corresponding
to the weak gravity limit of this theory. The effective bumblebee theory
displays new unconventional couplings between the bumblebee field and its field
strength, and the $U(1)$ gauge field along with its respective field strength,
as a result of the non-metricity effects. Thus, being a new gauge-bumblebee
theory, it represents an example of vector-vector couplings which are very
rarely considered, if not entirely overlooked, in the Abelian case. For this
theory we calculate the lower perturbative corrections. We close the paper with
discussions of other possible vector-vector couplings.
