I try to describe a villainous Shakespearean character (4)
'villainous shakespearean character' is the definition.
(villain in Shakespeare's Othello)
'i try to describe a' is the wordplay.
'try' becomes 'go' (both can mean an attempt).
'to describe' indicates putting letters inside.
'igo' placed around 'a' is 'IAGO'.
(Other definitions for iago that I've seen before include "Othello's evil counsellor", "stage villain", "Organ stop", "Othello's ensign", "Othello's nemesis".)