Rest of newspaper oddly skipped (4)
I believe the answer is:
ease
'rest' is the definition.
(synonyms)
'of newspaper oddly skipped' is the wordplay.
'of' indicates anagramming the letters (the answer comes from or 'of' the letters).
'oddly skipped' indicates alternate letters (letters in odd-numbered positions removed).
The alternate letters of 'newspaper' are 'esae'.
'esae' is an anagram of 'EASE'.
(Other definitions for ease that I've seen before include "Freedom from hardship" , "Poise or leisure" , "Relieve or slacken" , "Allay" , "'Comfort, rest (4)'" .)