Make fun of flipping old pen (4)
I believe the answer is:
biro
'pen' is the definition.
(Biro is a make of pen)
'make fun of flipping old' is the wordplay.
'make fun of' becomes 'rib' (synonyms).
'flipping' shows that the letters should be reversed in order.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'rib' back-to-front is 'bir'.
'bir'+'o'='BIRO'
(Other definitions for biro that I've seen before include "Type of ballpoint pen" , "writer" , "Laszlo Jozsef -, ballpoint pen inventor" , "Lazlo -, ballpoint pen inventor" , "Pocket item" .)