Give mother a wry grin on the side (6)
I believe the answer is:
margin
'the side' is the definition.
(thesaurus)
'give mother a wry grin' is the wordplay.
'give' means one lot of letters go next to another.
'mother' becomes 'ma' (Ma is another word for mother or mum).
'a wry' indicates an anagram (I've seen this in other clues).
'grin' is an anagram of 'rgin'.
'ma'+'rgin' is 'MARGIN'.
'on' is the link.
(Other definitions for margin that I've seen before include "bank" , "Bound" , "Edge, border, fringe" , "Blank space around the edge" , "Blank space around a text" .)