Observe pretty sweetheart becoming quiet (6)
I believe the answer is:
comply
'observe' is the definition.
(thesaurus)
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for comply that I've seen before include "Act in accordance with someone's rules, commands or wishes" , "Toe the line" , "Conform to rules" , "Yield to the wishes of another" , "Extra runs; farewells" .)