Extend stage to include end of apron afterwards (8)
I believe the answer is:
lengthen
'extend' is the definition.
(I've seen this before)
'stage to include end of apron afterwards' is the wordplay.
'stage' becomes 'leg' ('leg' can be a synonym of 'stage'**).
'to include' means one lot of letters goes inside another.
'end of' suggests the final letters.
'afterwards' becomes 'then' (I've seen this before).
The final letter of 'apron' is 'n'.
'leg' going around 'n' is 'leng'.
'leng'+'then'='LENGTHEN'
(Other definitions for lengthen that I've seen before include "Make or become longer" , "Spin out" , "Protract" , "Stretch" , "Extend or draw out" .)