Rush to give attention to the central heating (4)
I believe the answer is:
tear
'rush' is the definition.
(tearing is a kind of rushing)
'attention to the central heating' is the wordplay.
'attention' becomes 'ear' (having someone's ear is having their attention).
'to' says to put letters next to each other (I've seen this in other clues).
'the central' means to look at the middle letters.
The middle of 'heating' is 't'.
'ear' put after 't' is 'TEAR'.
'to give' is the link.
(Other definitions for tear that I've seen before include "Small globule of sorrow" , "charge" , "Move quickly; pull apart" , "A drop of optical moisture" , "Shred" .)