Annoying liars oddly ignored by monarch (6)
I believe the answer is:
irking
'annoying' is the definition.
(I've seen this in another clue)
'liars oddly ignored by monarch' is the wordplay.
'oddly ignored' means one should take alternating letters (letters in odd-numbered positions removed).
'by' is a charade indicator (letters next to each other).
'monarch' becomes 'king' (king is a kind of monarch).
The alternate letters of 'liars' are 'ir'.
'ir'+'king'='IRKING'
(Other definitions for irking that I've seen before include "Irritating, vexing" , "Disgusting" , "Annoying, bothering" , "Annoying, irritating" .)