Good-looking girl gets ring — first sign of engagement (5)
I believe the answer is:
belle
'good-looking girl' is the definition.
(belle means a beautiful girl)
'ring first sign of engagement' is the wordplay.
'ring' becomes 'bell' (both can mean to call on the phone).
'first sign of' indicates taking the first letters.
The initial letter of 'engagement' is 'e'.
'bell'+'e'='BELLE'
'gets' is the link.
(Other definitions for belle that I've seen before include "Handsome lady of the Ball?" , "Lovely girl" , "Beautiful female" , "Attractive woman" , "Reigning beauty" .)