Drive from university rector, for example, after retirement (4)
I believe the answer is:
urge
'drive' is the definition.
(I've seen this before)
'university rector for example after retirement' is the wordplay.
'university' becomes 'u' (abbreviation for university).
'rector' becomes 'r'.
'for example' becomes 'eg' (short for 'exempli gratia', 'for example' in Latin).
'after retirement' says the letters should be written backwards.
'eg' in reverse letter order is 'ge'.
'u'+'r'+'ge'='URGE'
'from' is the link.
(Other definitions for urge that I've seen before include "Strongly encourage" , "Incite to action" , "Advise earnestly, encourage to go on" , "Strong, restless desire" , "'Spur on, encourage (4)'" .)