Children's favourite appearing in Stuyvesant adverts (5)
I believe the answer is:
santa
'children's favourite' is the definition.
(I've seen this before)
'in stuyvesant adverts' is the wordplay.
'in' indicates the answer is hidden within the clue.
'SANTA' is hidden in the letters of 'stuyvesant adverts'.
'appearing' acts as a link.
(Other definitions for santa that I've seen before include "Dad in a red and white outfit?" , "St Nicholas" , "Present bringer" , "patron at Christmas" , "He comes down chimney" .)