Claim to turn up, right and left (7)
I believe the answer is:
purport
'claim' is the definition.
(I know that purport is a more specific form of the action claim)
'turn up right and left' is the wordplay.
'turn' says the letters should be written in reverse.
'right' becomes 'r' (abbreviation).
'and' is a charade indicator (letters next to each other).
'left' becomes 'port' (left side of a ship - opposite of starboard).
'up' written backwards gives 'pu'.
'pu'+'r'+'port'='PURPORT'
'to' is the link.
(Other definitions for purport that I've seen before include "Spirit" , "Intended meaning" , "Meaning, substance" , "Pretend; meaning" , "Seem or claim (to be)" .)