One very small bird by church (5)
I believe the answer is:
titch
'one very small' is the definition.
(informal term for a short person)
'bird by church' is the wordplay.
'bird' becomes 'tit' (tit is a kind of bird).
'by' is a charade indicator (letters next to each other).
'church' becomes 'ch' (common abbreviation).
'tit'+'ch'='TITCH'
(Other definitions for titch that I've seen before include "One's very short" , "Small person" , "Small man (colloq.)" , "small one" , "Little one" .)