I think you are
A medicine, abbreviated calendar and a cop's criminal with verbal pause;
shortened sugar over retrograte Greek η
η is eta
retrograde makes it "ate", a likely word ending; assume this is charades
over -> on
shortened sugar -> gluc? fruct?
verbal pause is "um" or maybe "uh" or "eh"
cop's criminal -> ?
abbreviated calendar -> cal
Taking the cryptic-clues at face value, it looks like
A medicine [def.]; abbreviated calendar [CAL] + a cop's criminal [???] + verbal pause [UM?] + shortened sugar [GLUC?] + over [ON] + retrograde Greek η [ATE<]
which gives CAL???UM GLUC?ONATE
trading out GLUC for CARB - this is definition by example, but ok -
and seeing the obvious missing CI in calcium, give us:
CALCIUM CARBONATE (A medicine [def.]; abbreviated calendar [CAL] + a cop's criminal [CI]
+ verbal pause [UM] + shortened sugar [CARB] + over [ON]
+ retrograde Greek η [ATE<])
Wikipedia tells me a confidential or criminal informant (CI) is a thing, so that answers that too. Yay, learning!