Material for roofing the little church over there? (6)
I believe the answer is:
thatch
'material for roofing' is the definition.
(as in a thatched roof)
'the little church over there?' is the wordplay.
'little' means to remove the last letter (the word is not quite complete).
'church over there?' becomes 'atch' (I can't explain this - if you can you should give a lot more credence to this answer).
'the' with its final letter taken off is 'th'.
'th'+'atch'='THATCH'
(Other definitions for thatch that I've seen before include "Old-fashioned roof covering material" , "nothing of interest to thief wanting roof lead" , "Organic material for old rustic roof" , "Old roofing material" , "Alternative to lead roof" .)