Run off to see about getting limit (6)
I believe the answer is:
escape
'run off' is the definition.
(I've seen this in another clue)
'see about getting limit' is the wordplay.
'about' is an anagram indicator.
'getting' indicates putting letters inside.
'limit' becomes 'cap' (capping is a kind of limiting).
'see' anagrammed gives 'ese'.
'ese' going around 'cap' is 'ESCAPE'.
'to' acts as a link.
(Other definitions for escape that I've seen before include "Duck" , "issue" , "Get away from the strange EC peas" , "Evade" , "Manage to avoid" .)