Vale! Leaving disheartened, having failed (4)
I believe the answer is:
glen
'vale' is the definition.
(glen is a kind of vale)
'leaving disheartened having failed' is the wordplay.
'disheartened' suggests removing the centre.
'having failed' indicates anagramming the letters.
'leaving' with its centre removed is 'leng'.
'leng' anagrammed gives 'GLEN'.
(Other definitions for glen that I've seen before include "Scottish or Irish valley" , "Narrow secluded valley in mountains" , "Depression in Scotland" , "Scottish mountain valley" , "Narrow Scots valley" .)