Granny, for example, taking some thick notepaper (4)
I believe the answer is:
knot
'granny for example' is the definition.
(granny is a kind of knot)
'some thick notepaper' is the wordplay.
'some' says the answer is hidden in the clue (some parts of the word are used).
'KNOT' is hidden within 'thick notepaper'.
'taking' acts as a link.
(Other definitions for knot that I've seen before include "Tie, hitch" , "Fastening such as reef or granny" , "A sheepshank or bowline" , "Small group (of people); tied rope" , "Tie (or what is put in one?)" .)