Henry, at Open University, reading for a time (4)
I believe the answer is:
hour
'time' is the definition.
(unit of time)
'henry at open university reading' is the wordplay.
'henry' becomes 'H' (symbol for the unit of electrical inductance).
'at' is a charade indicator (letters next to each other).
'open university' becomes 'OU'.
'reading' becomes 'r' (one of the traditional three R's of education).
'h'+'ou'+'r'='HOUR'
'for a' acts as a link.
(Other definitions for hour that I've seen before include "60 14 acrosses" , "Time within day" , "A 24th of a day" , "occasion" , "See 20" .)