Exigent rhymes with:
diligent, indigent, agent, astringent, bagent, cogent, contingent, convergent, detergent, diligent, divergent, emergent, indigent, indulgent, insurgent, intelligent, intransigent, largent, legent, migent, negligent, neugent, nugent, pageant, pungent, reagent, regent, resurgent, sargeant, sargent, sergeant, sergent, stringent, tangent, urgent, vigeant
Exigent sounds like:
easement, echemende, eisenhut, eisenhuth, equanimity, escondido, escuchando, esmond, examined, exhumed