Search for someone’s mother and sister, keeping husband close to heart (7)
I believe the answer is:
manhunt
'search for someone's' is the definition.
(search for a man)
'mother and sister keeping husband close to heart' is the wordplay.
'mother' becomes 'ma' (Ma is another word for mother or mum).
'and' becomes 'n' (common abbreviation for 'and').
'sister keeping husband' becomes 'hun' (I can't explain this - if you can you should give a lot more credence to this answer).
'close to' suggests the final letters (the close/ending of).
The final letter of 'heart' is 't'.
'ma'+'n'+'hun'+'t'='MANHUNT'
(Other definitions for manhunt that I've seen before include "Pursuit of missing person" , "in which one wanted to be found?" , "Search for wanted person" , "Organised search for a fugitive" , "Search for criminal" .)