Records a pet running at school (5)
I believe the answer is:
tapes
'records' is the definition.
(taping is a kind of recording)
'a pet running at school' is the wordplay.
'running' is an anagram indicator.
'at' says to put letters next to each other.
'school' becomes 's' (**).
'a'+'pet'='apet'
'apet' anagrammed gives 'tape'.
'tape'+'s'='TAPES'
(Other definitions for tapes that I've seen before include "A spate of magnetic records" , "Magnetic strips for recording" , "Recordings" , "Long thin pieces of cloth or paper" , "Records - strips of material" .)