Catalyzes the epimerization of trans-4-hydroxy-L-proline (t4LHyp) to cis-4-hydroxy-D-proline (c4DHyp) in vitro, albeit with low efficiency. The physiological substrate may be different. Displays no proline racemase activity. trans-4-hydroxy-L-proline = cis-4-hydroxy-D-proline kcat is 0.064 sec(-1) for t4LHyp epimerization. Belongs to the proline racemase family.