Points to serious score (7)
I believe the answer is:
engrave
'score' is the definition.
(thesaurus)
'points to serious' is the wordplay.
'points' becomes 'en' (**).
'to serious' becomes 'grave' ('grave' can be a synonym of 'serious').
'en'+'grave'='ENGRAVE'
(Other definitions for engrave that I've seen before include "Carve (a design) into hard material" , "Etch" , "Mistakes" , "Inscribe by cutting" , "Cut or carve (a text)" .)