Clue: Slow NY lawyer put in charge of exchange (6)
Answer: ADAGIO
Explanation: Definition: Slow
 DA(abbrev. for "District Attorney", a lawyer in, say, NY/New York, USA, in the role of chief prosecutor) **contained in**(put in) AGIO(a charge/fee paid on the exchange of one currency to another).
Defn: A musical direction to play in … time.