Vigorous number to sing about Romeo (9)
I believe the answer is:
trenchant
'vigorous' is the definition.
('trenchant' can be a synonym of 'vigorous')
'number to sing about romeo' is the wordplay.
'number' becomes 'ten' (ten is a kind of number).
'to sing' becomes 'chant' (chanting is a kind of singing**).
'about' means one lot of letters goes inside another.
'romeo' becomes 'r' (phonetic alphabet: alpha, bravo, charlie etc.).
'ten'+'chant'='tenchant'
'tenchant' going around 'r' is 'TRENCHANT'.
(Other definitions for trenchant that I've seen before include "Showing keenness" , "caustic?" , "Incisive in expression" , "Forceful" , "Incisive in style" .)