Mass-separated ^{187}Ta_{114} in a high-spin isomeric state has been produced for the first time by multinucleon transfer reactions, employing an argon gas-stopping cell and laser ionization. Internal γ rays revealed a T_{1/2}=7.3±0.9 s isomer at 1778±1 keV, which decays through a rotational band with perturbations associated with the approach to a prolate-oblate shape transition. Model calculations show less influence from triaxiality compared to heavier elements in the same mass region. The isomer-decay reduced E2 hindrance factor f_{ν}=27±1 supports the interpretation that axial symmetry is approximately conserved.