The old man's second to overtake (4)
I believe the answer is:
pass
'overtake' is the definition.
('pass' can be a synonym of 'overtake')
'the old man's second' is the wordplay.
'the old man's' becomes 'pas' ('pa' can be a synonym of 'old man'**).
'second' becomes 's' (common abbreviation).
'pas'+'s'='PASS'
'to' is the link.
(Other definitions for pass that I've seen before include "while away" , "Amatory advance" , "Progress" , "change" , "Eg, Khyber, Brenner" .)