Stamp showing this person's image (7)
I believe the answer is:
imprint
'stamp' is the definition.
(imprint is a kind of stamp)
'this person's image' is the wordplay.
'this person's' becomes 'im' (this person means the crossword setter themselves).
'image' becomes 'print' (I have seen 'Photographic image ' mean 'print' so perhaps 'image' could also mean 'print').
'im'+'print'='IMPRINT'
'showing' acts as a link.
(Other definitions for imprint that I've seen before include "Stamp; impression" , "Fix in the mind; stamp" , "Stamp (with sense of identity)" , "Stamp; brand" , "Mark made by pressing or stamping surface" .)