Player unhappy about each period of extra time (4,4)
I believe the answer is:
leap year
'period of extra time' is the definition.
(longer than a normal year)
'player unhappy about each' is the wordplay.
'unhappy' indicates anagramming the letters.
'about' is an insertion indicator.
'each' becomes 'ea' (abbreviation).
'player' anagrammed gives 'leapyr'.
'leapyr' placed around 'ea' is 'LEAP-YEAR'.
(Other definitions for leap year that I've seen before include "when summer Olympics are held?" , "Two thousand and four the next one" , "2008? - with 24d" , "The longest period of 12 months" , "such as 1984" .)