Allow John to start to investigate flies (3)
I believe the answer is:
let
'allow john' is the definition.
'let' can be an answer for 'allow' (synonyms). I am unsure of the 'john' bit.
'to start to investigate flies' is the wordplay.
'start' suggests taking the first letters.
'to' is a charade indicator (letters next to each other) (I've seen this in other clues).
'investigate flies' becomes 'le' (I can't justify this - if you can you should give a lot more credence to this answer).
The first letter of 'to' is 't'.
't' after 'le' is 'LET'.
(Other definitions for let that I've seen before include "Rent out: grant" , "Rent out (property)" , "Permit or rent" , "inefficient service" , "Umpire's decision" .)