Up in Rhyl, Noel's alone (4)
I believe the answer is:
only
'alone' is the definition.
(I know that alone can be written as only)
'up in rhyl noel's' is the wordplay.
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'in' indicates a hidden word.
'ylno' can be found hidden inside 'rhyl noels'.
'ylno' back-to-front is 'ONLY'.
(Other definitions for only that I've seen before include "Unique; merely" , "Alone; solitary" , "Mere" , "Solely; except that" , "Solely, lone" .)