Catalyzes the epimerization of trans-4-hydroxy-L-proline (t4LHyp) to cis-4-hydroxy-D-proline (c4DHyp). Is likely involved in a degradation pathway that converts t4LHyp to alpha-ketoglutarate. Can also catalyze the epimerization of trans-3-hydroxy-L-proline (t3LHyp) to cis-3-hydroxy-D-proline (c3DHyp), albeit with 170-fold lower efficiency. Displays no proline racemase activity. trans-4-hydroxy-L-proline = cis-4-hydroxy-D-proline kcat is 89 sec(-1) for t4LHyp epimerization. kcat is 2.4 sec(-1) for t3LHyp epimerization. Belongs to the proline racemase family.