"une fois" meaning "once"

[alan gould]

i have the sentence 

une fois l'ambulance partie, la foule s'est disperse'e.  the crowd dispersed once the ambulance had left.  

i'm surprised the verb "etre" doesn't precede "partie."  is this a set grammatical rule that's triggered by "une fois..."?  

merci

[George Hunt]

It's a set expression  and a "shortcut" as there are alternative  and more "long winded" ways of saying the same thing.

"Aussitot que"  + a verb comes to mind. ="as soon as"

https://www.lawlessfrench.com/subjunctivisor/aussitot-que/

and

https://forum.wordreference.com/threads/fr-aussit%C3%B4t-que-mode.2...

"dès que" is also nice (but I have never used it

https://en.wiktionary.org/wiki/d%C3%A8s_que