Motivated by the prospects of the ongoing B meson experiments, we study the exclusive $B \to a_1 (1260) \ell^- \bar{\nu}_\ell$ process within the Standard model effective field theory formalism. The new physics parameters are constrained by using the experimental branching fractions of the (semi)leptonic $B \to \ell \bar{\nu}$ and $B \to (\pi, \rho, \omega) \ell \bar{\nu}$ processes (where $\ell = e, \mu, \tau$) which undergoes $b \to u \ell \bar{\nu}$ quark level transitions. We then study a comprehensive angular coefficient analysis of the exclusive $B \to a_1 (1260) \ell^- \bar{\nu}_\ell$ process in the Standard model and in the presence of various new physics operators.