Deliver a homily, quietly gaining measure of influence (6)
I believe the answer is:
preach
'deliver a homily' is the definition.
(homily means a sermon or lecture)
'quietly gaining measure of influence' is the wordplay.
'quietly' becomes 'p' (musical symbol).
'gaining' says to put letters next to each other.
'measure of influence' becomes 'reach' (reach can mean influence or impact).
'p'+'reach'='PREACH'
(Other definitions for preach that I've seen before include "Lecture" , "Publicly proclaim" , "''Practise what you . . . . . . ''" , "Give a religious address" , "Moralise" .)