Disheartened teacher carries out religious pamphlets (6)
I believe the answer is:
tracts
'religious pamphlets' is the definition.
(I've seen this in another clue)
'disheartened teacher carries' is the wordplay.
'disheartened' means to remove the middle letters (the middle or heart is removed).
'carries' becomes 'acts' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'teacher' with its middle taken out is 'tr'.
'tr'+'acts'='TRACTS'
'out' is the link.
Can you help me to learn more?
(Other definitions for tracts that I've seen before include "Extended areas of land" , "Expanses of land or pamphlets" , "Big areas of land or small pamphlets" , "Plots" , "Large areas of land or small pamphlets" .)