信望 credit●influence●prestige●repute

信望がある have prestige 【形】popular

信望がある〔人に〕 enjoy someone's confidence

信望をなくす lose one's confidence

信望を高める〔~の〕 raise the prestige of

信望を高める〔人の〕 increase [add to, boost, enhance, improve, raise] someone's prestige

信望を失う lose one's confidence

信望を失う〔人の〕 forfeit someone's confidence

信望を喪失する lose one's confidence

信望を得る gain prestige

信望を得る〔人の〕 win someone's good opinion