Declare arrival of girl — not much to follow (8)
I believe the answer is:
announce
'declare arrival of' is the definition.
(as in announcing the arrival of guests)
'girl not much to follow' is the wordplay.
'girl' becomes 'ann' (woman's name).
'not much' becomes 'ounce' (an ounce of something is a small amount of it).
'to follow' is a charade indicator (letters next to each other).
'ann'+'ounce'='ANNOUNCE'
(Other definitions for announce that I've seen before include "Make known, declare" , "Make known publicly or to an audience" , "Declare, proclaim" , "Formally declare" , "Make known officially" .)