Esteem's rhymes with:
steams, steams, team's, teams, teams', teems, basim's, beam's, beams, creams, deems, dreams, eames, extremes, gleams, hakeem's, hakim's, hiems, kareem's, nemes, pezim's, racemes, reames, reams, redeems, regime's, regimes, reims, schemes, screams, seams, seems, siems, steams, streams, supremes, team's, teams, teams', teems, themes, weems
Esteem's sounds like:
ecosystems, eighteen's, eighteens, ejecting, equating, equations, estonians, exacting, exactions, exceeding, exciting, executing, executions, exhausting, existence, existing, exiting, extinguish, exuding