Figure a demented liar is out to be a competitor (5)
I believe the answer is:
rival
'a competitor' is the definition.
(I know that competitor can be written as rival)
'figure a demented liar is out' is the wordplay.
'figure' becomes 'v' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'a demented' is an anagram indicator.
'is out' is an insertion indicator.
'liar' with letters rearranged gives 'rial'.
'v' going into 'rial' is 'RIVAL'.
'to be' is the link.
Can you help me to learn more?
(Other definitions for rival that I've seen before include "Contender" , "Compete with" , "Contestant you hope to defeat" , "Someone you hope to defeat" , "Be equal to in quality" .)