Seeing American lawyer can start to grind (6)
I believe the answer is:
dating
'seeing' is the definition.
('date' can be a synonym of 'see')
'american lawyer can start to grind' is the wordplay.
'american lawyer' becomes 'DA' (abbreviation for 'District Attorney').
'can' becomes 'tin' (both are metal containers).
'start to' says to take the initial letters.
The initial letter of 'grind' is 'g'.
'da'+'tin'+'g'='DATING'
(Other definitions for dating that I've seen before include "Taking out" , "Going steady" , "Imposing time code or keeping social engagement" , "Seeing" , "Going out with (a person)" .)