Complex sentence: Dissatisfied with his progress at the firm, Littleton arranged with a Brooklyn judge to obtain some appointments defending indigent prisoners, and in so doing came to the attention of the local Kings County district attorney's office, who eventually hired him.
Split into simpler sentences: Dissatisfied with his progress at the firm, Littleton asked a Brooklyn judge to appoint him as defense counsel for some indigent prisoners. His success in defending the prisoners brought him to the attention of the local Kings County district attorney's office, who hired him.