Servant shortage disheartened Emily (6)
I believe the answer is:
lackey
'servant' is the definition.
(a lackey is a servant or assistant)
'shortage disheartened emily' is the wordplay.
'shortage' becomes 'lack' (a lack is a shortage of something).
'disheartened' suggests removing the centre (the middle or heart is removed).
'emily' with its centre taken out is 'ey'.
'lack'+'ey'='LACKEY'
(Other definitions for lackey that I've seen before include "Liveried servant" , "An old servant or slavish person" , "A servile follower or old servant" , "An archaic menial or servant" , "Flunkey, sycophant" .)