Clue: Illyrian gentleman's widow regularly off in pursuit of a scoundrel (5)
Answer: CURIO
Explanation: Definition: Illyrian gentleman

(w)**I**(d)**O**(w) [*regularly off*] *in pursuit of* **CUR **("a scoundrel")
 
*In Shakespeare's *Twelfth Night*, which is set in Illyria, Curio was an attendant of Orsino.