Significance of claim (7)
I believe the answer is:
purport
I believe this is a double definition.
'significance' is the first definition.
(purport is a kind of significance)
'claim' is the second definition.
(purporting is a kind of claiming)
'of' acts as a link.
(Other definitions for purport that I've seen before include "Spirit" , "Seem or claim (to be)" , "Pretend; meaning" , "Intended meaning" , "Meaning, substance" .)