Our being in the hot sun for ages (5)
I believe the answer is:
hours
'ages' is the definition.
(hour can mean an age or era)
'our being in the hot sun' is the wordplay.
'being in' means one lot of letters goes inside another.
'the hot' becomes 'h' (abbreviation, eg on taps).
'sun' becomes 'S' (abbreviation).
'h'+'s'='hs'
'our' placed within 'hs' is 'HOURS'.
'for' acts as a link.
(Other definitions for hours that I've seen before include "time appointed for work" , "Periods of time" , "Matins and Vespers, say?" , "A long time" .)