The fine folk who investigate crimes have many standard abbreviations to define their profession, much to the delight of the crossword setter. If the word "detective" or its like appears in a clue, the usual suspects in the answer are:
TEC Informal short form of "detective"
Times 24226: One who investigates metal, say, specialising in applied science (9) TECHNICAL
sounds like TEC (one who investigates) NICKEL (metal, say)
DI Abbreviation of Detective Inspector, a UK police rank. This is common in words starting with DIS-.
Times 24588: Banish investigator before short tour of duty (6) DISPEL
DI (investigator) SPEL[l] (tour of duty, shortened)
DS Abbreviation of Detective Sergeant, a UK police rank. Usually occurs in the middle of the answer.
Guardian 25083 (Araucaria): Detective on wheels has instrument for cheat (9) CARDSHARP
DS (detective) on CAR (wheels), plus HARP (instrument)
PI Abbreviation of Private Investigator, also called Private Eye
FT 13415 (Viking): Detective's question linked to drug offence (5) PIQUE
PI (detective) QU (question) E (drug)
BUSY Slang for detective
Times 24583: Character coming last busy entering a second race (6) AZTECS
Z (character coming last) TEC (busy), in A S (second)
DICK Informal short form of "detective"
Times 24388: Detective mounted routine trap for outlaw (4,6) DICK TURPIN
DICK (detective), RUT (routine) reversed, PIN (trap)
To add to that are many detectives from fiction with grid-friendly names. Such as:
FT 13433 (Cincinnus): In novel form, I'm great detective (7) MAIGRET
Anagram of (IMGREAT), &lit. The detective here is Jules Maigret, commissioner of the French Sûreté, created by author Georges Simenon.
The next appeared in the Times Crossword of 1st Feb 1940, republished on Times Crossword Club on the occasion of the crossword's 80th birthday this year.
Though "busy" in fiction, he suggests a decline in business (9) LESTRADE
Sounds like 'less trade'. Inspector Lestrade is the busy (detective) from Conan Doyle's Sherlock Holmes series.
If you aren't into detective fiction, this list from Wikipedia will help.
Times 24465: Dick gets round, limping about — right, will we wait for him? (9) L _ T _ _ _ _ _ R
Times 23435: Three points suppressed by detective writer (7) D _ _ _ _ _ S
Guardian 25029 (Araucaria): Old American sleuth pursuing extremes (5) A _ _ _ _
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