Stealing a sheet to put round the sick (7)
I believe the answer is:
pillage
'stealing' is the definition.
(I know that pillage is a type of looting)
'a sheet to put round the sick' is the wordplay.
'a sheet' becomes 'page' (sheet of paper).
'to put round' indicates putting letters inside.
'the sick' becomes 'ill' (I've seen this before).
'page' enclosing 'ill' is 'PILLAGE'.
(Other definitions for pillage that I've seen before include "Sacking" , "Violent stealing" , "Rob with violence" , "Loot" , "Plunder, sack" .)