Fold the first pieces of crêpe paper around the edge (5)
I believe the answer is:
crimp
'fold' is the definition.
(I know that fold can be written as crimp)
'first pieces of crepe paper around the edge' is the wordplay.
'first pieces of' says to take the initial letters (I've seen 'first piece of' mean this).
'around' indicates putting letters inside.
'the edge' becomes 'rim' (rim is a kind of edge).
The first letters of 'crepe paper' is 'cp'.
'cp' going around 'rim' is 'CRIMP'.
'the' acts as a link.
(Other definitions for crimp that I've seen before include "Connect by squeezing together" , "wave" , "Bend into shape" , "Compress into small folds or ridges" , "Curl hair tightly" .)