  Since current challenges faced by $\Lambda$CDM might be hinting at new
unravelled physics, here we investigate a plausible cosmological model where a
vector field acts as source of dark energy. In particular, we examine whether
an energy-momentum exchange between dark energy and dark matter could provide
an explanation for current discrepancies in cosmological parameters. We
carefully work out equations governing background and linear order
perturbations and implement them in a Boltzmann code. We found that a negative
coupling makes the dark energy equation of state less negative and closer to a
cosmological constant during the matter dominated epoch than an uncoupled
vector dark energy model. While the effect of the coupling is hardly noticeable
through its effect on matter density perturbations, matter velocity
perturbations and gravitational potentials are enhanced at late-times when dark
energy dominates. Therefore, data of redshift space distortions help to narrow
down these kinds of couplings in the dark sector. We computed cosmological
constraints and found common parameters also present in $\Lambda$CDM are in
good agreement with the Planck Collaboration baseline result. Our best fit for
a negatively coupled vector field predicts a higher growth rate of matter
perturbations at low redshift, thus exacerbating the disagreement with redshift
space distortions data. While a positively coupled vector field can lead to
power suppression of $P_{\rm{m}}(k,z=0)$ on small scales as well as a lower
growth rate of matter perturbations than the standard model, it might
compromise the goodness of fit to the CMB angular power spectrum on small
scales. We conclude that our negatively coupled vector dark energy model does
not solve current tensions (i.e., $H_0$ and $\sigma_8$). (abridged)
