Old man should cover chest in something warm (5)
I believe the answer is:
parka
'something warm' is the definition.
(parka is a warm coat)
'old man should cover chest' is the wordplay.
'old man' becomes 'pa' (both can mean father).
'should cover' indicates putting letters inside.
'chest' becomes 'ark' (historical term for a chest).
'pa' placed around 'ark' is 'PARKA'.
'in' is the link.
(Other definitions for parka that I've seen before include "Hooded warm jacket" , "Weatherproof jacket with hood" , "hoodie" , "Anorak" , "weatherproof cover" .)