Improper accessory? Hold on, teachers work here (9,6)
I believe the answer is:
secondary school
'teachers work here' is the definition.
(place where teachers work)
'improper accessory? hold on' is the wordplay.
'improper' indicates an anagram.
'accessory'+'hold'+'on'='accessoryholdon'
'accessoryholdon' with letters rearranged gives 'SECONDARY SCHOOL'.
(Other definitions for secondary school that I've seen before include "Educational establishment" , "Where youth's instructed" .)