First investigation into the 'loud robber' (5)
I believe the answer is:
thief
'robber' is the definition.
(both can mean someone who steals)
'first investigation into the loud' is the wordplay.
'first investigation' becomes 'i' (1st letter of 'investigation').
'into' means one lot of letters goes inside another.
'loud' becomes 'f' (short for forte - 'loud' in music).
'i' inserted inside 'the' is 'thie'.
'thie'+'f'='THIEF'
(Other definitions for thief that I've seen before include "Burglar, say" , "Crook" , "Raffles, say" , "nicker?" , "Unlawful taker" .)