Dog drinking drop of one's tea (5)
I believe the answer is:
pekoe
'tea' is the definition.
(pekoe is a kind of tea)
'dog drinking drop of one's' is the wordplay.
'dog' becomes 'peke' (Peke is an example**).
'drinking' means one lot of letters goes inside another.
'drop of' suggests taking the first letters.
The first letter of 'ones' is 'o'.
'peke' placed around 'o' is 'PEKOE'.
(Other definitions for pekoe that I've seen before include "Superior grade of black tea" , "Type of black tea" , "brew" , "Scented black tea" , "Thin mark; run naked" .)