Your and my period of time on radio (3)
I believe the answer is:
our
'your and my' is the definition.
(I've seen this before)
'period of time on radio' is the wordplay.
'period of time' becomes 'hour' (hour is a kind of period of time).
'on radio' indicates a 'sounds like' (homophone) clue.
'hour' sounds like 'OUR'.
(Other definitions for our that I've seen before include "Relating to us" , "''Now is the winter of ... discontent'' (Richard III)" , "'-- House' (Madness song)" , "group possession?" , "Yours and mine" .)