Having knocked back drink after drink, speak indistinctly (6)
I believe the answer is:
murmur
'speak indistinctly' is the definition.
('murmur' can be a synonym of 'speak indistinctly')
'having knocked back drink' is the wordplay.
'having' becomes 'mur' (I can't justify this - if you can you should give a lot more credence to this answer).
'knocked back' is a reversal indicator.
'drink' becomes 'rum' (I've seen this before).
'rum' back-to-front is 'mur'.
'mur'+'mur'='MURMUR'
'after drink' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for murmur that I've seen before include "Little noise" , "Low, indistinct speech" , "Soft voices (of discontent)" , "Subdued complaint" , "Quietly spoken utterance; heart defect" .)