Definitely not old, female in close (2,4)
I believe the answer is:
no fear
'definitely not' is the definition.
(I've seen this before)
'old female in close' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'female' becomes 'f' (abbreviation).
'in' is an insertion indicator.
'close' becomes 'near' (similar in meaning).
'o'+'f'='of'
'of' placed inside 'near' is 'NO FEAR'.
(Other definitions for no fear that I've seen before include "what the bold show" , "Never" , "Definitely not (informal)" , "Far one (anag.)" , "Certainly not (informal)" .)