Dog drinks old tea (5)
I believe the answer is:
pekoe
'tea' is the definition.
(pekoe is a kind of tea)
'dog drinks old' is the wordplay.
'dog' becomes 'peke' (Peke is an example**).
'drinks' means one lot of letters goes inside another.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'peke' going around 'o' is 'PEKOE'.
(Other definitions for pekoe that I've seen before include "Type of black tea" , "High-quality black tea" , "Thin mark; run naked" , "Variety of black tea" , "brew" .)