Throw out old book about the country (4)
I believe the answer is:
oust
'throw out' is the definition.
(I know that throw out can be written as oust)
'old book about the country' is the wordplay.
I cannot really see how this works, but
'old' could be 'o' (common abbreviation eg in OE for Old English) and 'o' is found in the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is found within the answer.
'country' could be 'us' (US is an example) and 'us' is found in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for oust that I've seen before include "Extract" , "Expel from office or position" , "Put out, say of office" , "Expel - eject" , "Force out; supplant" .)