Why is être used here and not avoir?

Paul, this is not a verb conjugation of prendre in passé composé which would need auxiliary ‘avoir’,  but the verb ‘être’ in the present tense followed by the past participle of prendre as adjective ‘prises’ (agreement with plural feminine noun ‘places’). 

In English ‘ All the parking places/spaces are taken ‘ 

 https://progress.lawlessfrench.com/revision/glossary/verbal/le-participe-passe-past-participle

 https://www.wordreference.com/fren/prise