Attorney outside of the court (4)
I believe the answer is:
date
'court' is the definition.
(romantically pursue)
'attorney outside of the' is the wordplay.
'attorney' becomes 'da' (District Attorney).
'outside of' says to hollow out the word (remove centre letters).
'the' with its middle removed is 'te'.
'da'+'te'='DATE'
(Other definitions for date that I've seen before include "Particular day" , "one's arranged to meet" , "A social appointment - check calendar" , "The fruit for a social engagement" , "Specified day" .)