Having smuggled in drugs, a Mafia leader on Alcatraz moving cell (6)
'moving cell' is the definition.
(single-celled organism capable of moving)
'having smuggled in drugs a mafia leader on alcatraz' is the wordplay.
'having smuggled in' indicates putting letters inside.
'drugs' becomes 'e' (somebody 'on E' could also be 'on drugs').
'mafia' becomes 'mob' (informal term for the mafia).
'leader on' indicates taking the first letters (the letter which leads the word).
The first letter of 'alcatraz' is 'a'.
'e' placed into 'amob' is 'amoeb'.
(Other definitions for amoeba that I've seen before include "Unicellular creature", "Single-celled animal", "O, Mam, be a one-celled animal", "Not much life", "parasitic type".)