Seeing District Attorney can lead to grief (6)
I believe the answer is:
dating
'seeing' is the definition.
('date' can be a synonym of 'see')
'district attorney can lead to grief' is the wordplay.
'district attorney' becomes 'da' ('D.A.' can be a synonym of 'district attorney').
'can' becomes 'tin' ('tin' can be a synonym of 'can').
'lead to' says to take the initial letters.
The initial letter of 'grief' is 'g'.
'da'+'tin'+'g'='DATING'
(Other definitions for dating that I've seen before include "Establishing the age of" , "Taking out" , "Imposing time code or keeping social engagement" , "Going steady" , "Going out with (a person)" .)