Support Reds, playing in high temperature (8)
I believe the answer is:
headrest
'support' is the definition.
(headrest is a kind of support)
'reds playing in high temperature' is the wordplay.
'playing' is an anagram indicator.
'in' is an insertion indicator.
'high temperature' becomes 'heat' ('heat' can be a synonym of 'high temperature').
'reds' with letters rearranged gives 'dres'.
'dres' placed inside 'heat' is 'HEADREST'.
(Other definitions for headrest that I've seen before include "Capital supporter" , "support to chairman?" , "Cushion on top of car seat" , "With capital support" , "Chair back support" .)