During burlesque, a keen one takes peep (6)
I believe the answer is:
squeak
'peep' is the definition.
(thesaurus)
'during burlesque a keen one' is the wordplay.
'during' says the answer is hidden in the clue.
'SQUEAK' is hidden in the letters of 'burlesque a keen one'.
'takes' acts as a link.
(Other definitions for squeak that I've seen before include "High-pitched animal noise - (narrow) escape" , "(Succeed by) a narrow margin" , "Short, high-pitched sound" , "Sound of a mouse" , "Short high-pitched cry as of mouse" .)