Since we know that the NSA collects internet traffic and email, why can't president Trump just ask the NSA for a copy of Hillary's deleted emails? They weren't on an encrypted government system so would have looked like private citizen emails.
Hillary Clinton is no longer a politically relevant opponent. Trump has little to gain by persecuting her further. He has more important opponents to deal with.
Even if there is something to find, what the NSA does is warrantless wiretapping. Whatever information is obtain that way is inadmissible in a court of law. It could be used to sway the public opinion, but as previously mentioned there is little reason to do that.
It would look dangerously similar to the actions of Richard Nixon. Nixon also used federal law enforcement and intelligence resources to harass and surveil political opponents. When this became public, it became known as the Watergate Scandal. Nixon was forced to resign.