Very small container by end of alleyway (4)
I believe the answer is:
tiny
'very small' is the definition.
(I've seen this before)
'container by end of alleyway' is the wordplay.
'container' becomes 'tin' (tin is a kind of container).
'by' means one lot of letters go next to another.
'end of' indicates one should take the final letters.
The last letter of 'alleyway' is 'y'.
'tin'+'y'='TINY'
(Other definitions for tiny that I've seen before include "Little" , "pocket" , "Minuscule" , "Miniscule" , "Diminutive; small" .)