Beer or, at the day centre, milk (4)
I believe the answer is:
pint
'beer' is the definition.
(beer is typically served by the pint)
'at the day centre milk' is the wordplay.
I cannot quite see how this works, but
'at' could be 'in' (synonymous in some cases - eg at school, in school) and 'in' is found in the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is present in the answer.
A single letter 'p' remains which might be clued in a way I don't see.
This explanation may well be incorrect...
'or' is the link.
Can you help me to learn more?
(Other definitions for pint that I've seen before include "Imperial measure of capacity" , "One eighth of a gallon" , "Quantity" , "Measure of the plain man's alcoholic drink" , "Half a quart" .)