Building by the church provides little shelter (5)
I believe the answer is:
hutch
'little shelter' is the definition.
'hutch' can be an answer for 'shelter' (hutch is a kind of shelter). I am not certain of the 'little' bit.
'building by the church' is the wordplay.
'building' becomes 'hut' (I've seen this before).
'by' means one lot of letters go next to another.
'the church' becomes 'ch' (common abbreviation).
'hut'+'ch'='HUTCH'
'provides' is the link.
Can you help me to learn more?
(Other definitions for hutch that I've seen before include "Rabbit residence" , "Cage for rabbit?" , "Cage for small animals" , "Domesticated rabbit's home" , "where rabbit lives?" .)