Fake national symbol? Not half (4)
I believe the answer is:
sham
'fake' is the definition.
('sham' can be a synonym of 'fake')
'national symbol? not half' is the wordplay.
'national symbol?' becomes 'shamrock' (symbol of Ireland).
'not half' indicates taking half.
'shamrock' with half the letters taken is 'SHAM'.
(Other definitions for sham that I've seen before include "Feign" , "Pretence, hoax" , "Counterfeit, fake" , "Mash, being false" , "Pretense; bogus" .)