Background: Nuclear structure near the N = 50 shell closure above 78Ni provides essential information on shell evolution, the persistence of magicity, and the ongoing discussion of shape coexistence in this region. The nucleus 84Br serves as an important benchmark for shell-model interactions describing nuclides near the N = 50 shell closure above 78Ni. Purpose: The purpose of this work is to investigate the low-spin structure of 84Br populated via the β-decay of 84Se, and to benchmark different shell-model interactions and Hartree-Fock second Tamm-Dancoff approximation (HF-STDA) calculations, with particular emphasis on the role of cross-shell excitations across the N = 50 shell gap. Methods: The β-decay of 84Se was studied at the LOHENGRIN recoil separator at the Institut Laue-Langevin (ILL), where 84Se was produced via thermal-neutron-induced fission of 235U. Two complementary experimental setups were employed: (i) a high-efficiency setup consisting of two HPGe clover detectors and a Si(Li) detector for γ-ray and conversion electron spectroscopy, and (ii) a β fast-timing setup using LaBr3(Ce) and plastic scintillator detectors for excited state lifetime measurement. Results: A new excited state in 84Br at 906 keV was identified. The log10 f t values for the Gamow-Teller transitions to the known 1+1 state and the newly observed state were measured as 4.06(2) and 4.91(9), respectively. The lifetime of the 1+1 state was determined to be τ = 77(11) ps, while an upper limit of τ < 20 ps was established for the newly observed state. The spin-parity of the newly observed state is assigned as Jπ = 1+2 based on the measured log10 f t value and lifetime. Conclusions: Large-scale shell-model calculations were performed using the widely used JUN45, jj44b, and jj4-45-KS interactions, the latter incorporating up to one-particle and one-hole cross-shell excitation across the N = 50 shell closure. HF-STDA calculations were also performed and compared with experimental data, providing complementary information to shell-model calculations. Shell-model calculations including cross-shell excitations presented an improved agreement with the experimental log10 f t values, indicating that cross-shell correlations play a non-negligible role in describing the structure of nuclei near the N = 50 shell closure.