Eliot carrying that woman's second hot water bottle (7)
I believe the answer is:
thermos
'hot water bottle' is the definition.
(container for keeping drinks hot)
'eliot carrying that woman's second' is the wordplay.
'eliot' becomes 'ts' (poet TS Eliot).
'carrying' indicates putting letters inside.
'that woman's' becomes 'her' (belonging to a woman).
'second' becomes 'mo' (both are short periods of time).
'her'+'mo'='hermo'
'ts' enclosing 'hermo' is 'THERMOS'.
(Other definitions for thermos that I've seen before include "Vacuum flask for mothers" , "Container to retain heat" , "Heat-retaining flask for mothers" , "Flask trade mark" .)