Sheepish journalist follows fake eatery up (10)
I believe the answer is:
shamefaced
'sheepish' is the definition.
('shamefaced' can be a synonym of 'sheepish')
'journalist follows fake eatery up' is the wordplay.
'journalist' becomes 'ed' (short for editor).
'follows' is a charade indicator (letters next to each other).
'fake' becomes 'sham' ('sham' can be a synonym of 'fake'**).
'eatery' becomes 'cafe'.
'up' is a reversal indicator (in down clue: letters go upwards).
'cafe' reversed gives 'efac'.
'sham'+'efac'='shamefac'
'ed' put after 'shamefac' is 'SHAMEFACED'.
(Other definitions for shamefaced that I've seen before include "Hangdog" , "Abashed" , "Looking humiliated" , "became conscience-stricken" , "Showing guilty embarrassment" .)