There's remarkably little info about the process by which one can acquire a time-turner. Not only does the Ministry jealously guard them on their own premises but there's evidently a strict procedure needed in order to get hold of one.
The user must be of impeccable character
The user must not use it to aggrandise themselves
The user (if underage) must be vouched for by a senior wizard. In Hermione's case both McGonagall and Dumbledore are evidently involved in her getting the time-turner.
The time-turner is for use for a limited period only, to achieve a specified goal.
Abusing the time-turner is punishable (punishment not known).
‘It’s called a Time-Turner,’ Hermione whispered, ‘and I got it from Professor McGonagall on our first day back. I’ve been using it all year to get to all my lessons. Professor McGonagall made me swear I wouldn’t tell anyone. She had to write all sorts of letters to the Ministry of Magic so I could have one. She had to tell them that I was a model student, and that I’d never, ever use it for anything except my studies … I’ve been turning it back so I could do hours over again, that’s how I’ve been doing several lessons at once, see? But …