High spin band structures of neutron-rich $^{152-158}$Pm isotopes have been obtained from the measurement of prompt $gamma$-rays of isotopically identified fragments produced in fission of $^{238}$U+$^{9}$Be and detected using the VAMOS++ magnetic spectrometer and EXOGAM segmented Clover array at GANIL and also from the high statistics $gamma$-$gamma$-$gamma$ and $gamma$-$gamma$-$gamma$-$gamma$ data from the spontaneous fission of $^{252}$Cf using Gammasphere. The excited states in $^{157}$Pm and those above the isomers in even-A Pm isotopes $^{152,154,156,158}$Pm have been identified for the first time. The spectroscopic information on the rotational band structures in odd-A Pm isotopes has been extended considerably to higher spins and the possibility of the presence of reflection asymmetric shapes is explored. The configuration assignments are based on the results of Cranked Relativistic Hartree-Bogoliubov calculations. From the systematics of bands in odd-A Pm isotopes and weak population of opposite parity bands, octupole deformed shapes in neutron rich Pm isotopes beyond $N=90$ seem unlikely to be present.
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