Peter is spoiling period of rest (7)
I believe the answer is:
respite
'period of rest' is the definition.
'respite' can be an answer for 'rest' (synonyms). I am not certain of the 'period of' bit.
'peter is spoiling' is the wordplay.
'spoiling' is an anagram indicator.
'peter'+'is'='peteris'
'peteris' with letters rearranged gives 'RESPITE'.
Can you help me to learn more?
(Other definitions for respite that I've seen before include "Short period of relief" , "Brief period of relief" , "interruption" , "Pause; reprieve" , "Hiatus" .)