Old fogey's beginning to get in close? Definitely not! (2,4)
I believe the answer is:
no fear
'definitely not' is the definition.
(I've seen this before)
'old fogey's beginning to get in close?' is the wordplay.
'beginning to' suggests taking the first letters.
'get in' is an insertion indicator.
'close?' becomes 'near' ('near' can be similar in meaning to 'close').
The initial letters of 'old fogeys' is 'of'.
'of' inserted into 'near' is 'NO FEAR'.
(Other definitions for no fear that I've seen before include "Certainly not (informal)" , "Definitely not (informal)" , "What 7 [INTREPID] person will have" , "Informally, certainly not., who's afraid" , "Very clear Five ac [REFUSAL]" .)