Aerospace facility’s court meeting originally taking a long time (7)
I believe the answer is:
woomera
'aerospace facility's' is the definition.
(Australian aerospace facility)
'court meeting originally taking a long time' is the wordplay.
'court' becomes 'woo' (both can mean to romance someone).
'originally' indicates taking the first letters.
'taking' says to put letters next to each other.
'a long time' becomes 'era' (a long period of time).
The first letter of 'meeting' is 'm'.
'woo'+'m'+'era'='WOOMERA'
(Other definitions for woomera that I've seen before include "South Australian town" , "Austr. rocket range" , "stick with extra ooph!" , "Aboriginal throwing stick; Australian rocket range" , "Aborigine spear stick" .)