Greeting detective, we hear, in advanced style (2,4)
I believe the answer is:
hi tech
'in advanced style' is the definition.
(with new technology)
'greeting detective we hear' is the wordplay.
'greeting' becomes 'hi' (hi is a kind of greeting).
'detective' becomes 'tec' (synonyms).
'we hear' indicates a 'sounds like' (homophone) clue.
'tec' is a homophone of 'tech'.
'hi'+'tech'='HI-TECH'
(Other definitions for hi tech that I've seen before include "Using sophisticated equipment" , "style of interior design" , "Making use of up-to-date resources" , "Extremely modern" , "with lots of gadgets" .)