Mark gets embarrassed or worried (8)
I believe the answer is:
badgered
'worried' is the definition.
(thesaurus)
'mark gets embarrassed' is the wordplay.
'mark' becomes 'badge' (badging is a kind of marking).
'gets' says to put letters next to each other.
'embarrassed' becomes 'red' (someone may blush or go red when embarrassed).
'badge'+'red'='BADGERED'
'or' acts as a link.
(Other definitions for badgered that I've seen before include "Pestered" , "hassled" , "Annoyed persistently" , "Harassed" , "chivvied" .)