Run, or jog, between times (4)
I believe the answer is:
trot
'run' is the definition.
(I know that trot is a more specific form of run)
'jog between times' is the wordplay.
'jog' becomes 'ro' (I am not sure about this - if you are sure you should believe this answer much more).
'between' indicates putting letters inside.
'times' becomes 'tt' (two abbreviations for time).
'ro' inserted into 'tt' is 'TROT'.
'or' is the link.
Can you help me to learn more?
(Other definitions for trot that I've seen before include "An elderly woman" , "Fairly brisk pace" , "A slowish run, often by horse" , "A slowish run, perhaps by horse" , "Old communist" .)