Deliver one booze half-heartedly, taking too much time about it (8)
I believe the answer is:
liberate
'deliver one booze half' is the definition.
'liberate' can be an answer for 'deliver' (thesaurus). I'm not certain of the 'one booze half' bit.
'heartedly taking too much time about it' is the wordplay.
'heartedly' becomes 'er' (I've seen this in other clues).
'taking too much time' becomes 'libate' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'about it' means one lot of letters goes inside another.
'er' put into 'libate' is 'LIBERATE'.
Can you help me to learn more?
(Other definitions for liberate that I've seen before include "Set free, rescue from bondage" , "Make free" , "let go" , "Set free, emancipate" , "Free (someone)" .)