Dropped off after a short time in a cot? (6)
I believe the answer is:
abated
'dropped off' is the definition.
(I've seen this before)
'a short time in a cot?' is the wordplay.
'short time' becomes 't' (abbreviation for time).
'in' is an insertion indicator.
'cot?' becomes 'bed' (cot is a kind of bed).
'a'+'t'='at'
'a'+'bed'='abed'
'at' put into 'abed' is 'ABATED'.
'after' acts as a link.
(Other definitions for abated that I've seen before include "Lowered" , "Eased" , "weakened" , "Settled" , "Went down and calmed like stormed" .)