A record height (3)
I believe the answer is:
alp
'height' is the definition.
(as in the Alps - height can mean something high)
'a record' is the wordplay.
'record' becomes 'L-P' (abbreviation for long play record).
'a'+'lp'='ALP'
(Other definitions for alp that I've seen before include "Mountain pasture" , "high point" , "Swiss mountain" , "One of a European mountain range" , "Mont Blanc, for example" .)