Double tonic water initially put on the rocks (5)
I believe the answer is:
twice
'double' is the definition.
('twice' can be a synonym of 'double')
'tonic water initially put on the rocks' is the wordplay.
'initially' suggests taking the first letters.
'put on' says to put letters next to each other.
'the rocks' becomes 'ice' (I've seen this before**).
The first letters of 'tonic water' is 'tw'.
'tw'+'ice'='TWICE'
(Other definitions for twice that I've seen before include "You only live -- (film)" , "Two times" , "Doubly" , "Double in quantity" .)