Run away after writer gets girl (8)
I believe the answer is:
penelope
'girl' is the definition.
'run away after writer' is the wordplay.
'run away' becomes 'elope' (I've seen this before).
'after' says to put letters next to each other.
'writer' becomes 'pen' (I've seen this before).
'elope' put after 'pen' is 'PENELOPE'.
'gets' is the link.
(Other definitions for penelope that I've seen before include "Odysseus's wife" , "Mrs Odysseus" , "Wife of Odysseus or Ulysses" , "The wife who waited for years for Odysseus" , "Waiter" .)