Doctor, for example, beginning to swallow sediment (5)
I believe the answer is:
dregs
'sediment' is the definition.
(dregs is a kind of sediment)
'doctor for example beginning to swallow' is the wordplay.
'doctor' becomes 'dr' ('Dr' can be a synonym of 'doctor').
'for example' becomes 'eg' ('e.g.' can be a synonym of 'for example').
'beginning to' says to take the initial letters.
The initial letter of 'swallow' is 's'.
'dr'+'eg'+'s'='DREGS'
(Other definitions for dregs that I've seen before include "Most worthless parts" , "Sediment - rabble" , "Sediment at the bottom of a liquid" , "Remnant of drink" , "Grounds; refuse" .)