Close call at home -- hates to lose cover (9)
I believe the answer is:
terminate
'close' is the definition.
(I've seen this before)
'call at home hates to lose cover' is the wordplay.
'call' becomes 'term' (terming is a kind of calling**).
'at home' becomes 'in' ('in' can be similar in meaning to 'at home').
'to lose cover' says to take the centre.
The middle of 'hates' is 'ate'.
'term'+'in'+'ate'='TERMINATE'
(Other definitions for terminate that I've seen before include "Put an end to, finish" , "Bring to an end" , "Put an end to, discontinue" , "Stop" , "Close" .)