Clue: Honest priest found in cocktail bar by Luddite extremists (8)
Answer: RELIABLE
Explanation: Definition: Honest
ELI (Biblical "priest") inside RAB, plus extreme letters from L-uddit-E 
I think RAB as an anagram of "bar", with "cocktail" as a hint at 'mixing'
 
RAB could also be a reversal of "bar" – if "cock" can be read as in turn or lift, with tail referring to the bottom end of the word