Bookish detective with rules for system of communication (5,4)
I believe the answer is:
morse code
'system of communication' is the definition.
(communication code using lights or sound signals)
'bookish detective with rules' is the wordplay.
'bookish detective' becomes 'Morse' (Inspector Morse, in novels by Colin Dexter).
'with' is a charade indicator (letters next to each other).
'rules' becomes 'code'.
'morse'+'code'='MORSE CODE'
'for' is the link.
(Other definitions for morse code that I've seen before include "Dot and dash signals" , "Means of signalling by dots and dashes" , "A way to signal" , "Way of sending message" , "Means to communicate" .)