Quick-witted Republican leaving for bay (5)
I believe the answer is:
bight
'bay' is the definition.
(I've seen this before)
'quick-witted republican leaving' is the wordplay.
'quick-witted' becomes 'bright' (I've seen this before).
'republican' becomes 'r' (abbreviation).
'leaving' indicates named letters should be taken away.
'bright' with 'r' taken out is 'BIGHT'.
'for' acts as a link.
(Other definitions for bight that I've seen before include "Large broad bay -- middle part of a slack rope" , "loop of rope?" , "Bay, sounds like a morsel of food" , "Wide bay" , "Bay - bend in rope" .)