Measure period covered by recent broadcast (10)
I believe the answer is:
centimetre
'measure' is the definition.
(centimetre is a kind of measure)
'period covered by recent broadcast' is the wordplay.
'period' becomes 'time' (time is a kind of period).
'covered by' indicates putting letters inside.
'broadcast' indicates anagramming the letters.
'recent' with letters rearranged gives 'centre'.
'time' placed inside 'centre' is 'CENTIMETRE'.
(Other definitions for centimetre that I've seen before include "Short distance" , "About four tenths of an inch" , "not giving an inch then?" , "Hundredth of a metre" , "From a little distance" .)