Extremely pretty country brings burning desire (9)
I believe the answer is:
pyromania
'burning desire' is the definition.
(desire to burn)
'extremely pretty country' is the wordplay.
'extremely' suggests removing the centre (only the extremes of the word are used).
'country' becomes 'romania' (European country).
'pretty' with its middle removed is 'py'.
'py'+'romania'='PYROMANIA'
'brings' acts as a link.
(Other definitions for pyromania that I've seen before include "Fire-raising compulsion" , "setting of conflagration" , "Obsessive desire to start fires" , "lighting up for fun?" , "Flaming madness!" .)