Become quiet? Goodness! (4)
I believe the answer is:
gosh
'goodness' is the definition.
(both are expressions of surprise)
'become quiet?' is the wordplay.
'become' becomes 'go' (synonyms).
'quiet?' becomes 'sh'.
'go'+'sh'='GOSH'
(Other definitions for gosh that I've seen before include "Cor!" , "expression of surprise" , "Surprised exclamation" , "Exclamation of surprise" , "Good heavens!" .)