Recording a pet running (4)
I believe the answer is:
tape
'recording' is the definition.
(I know that tape is a type of recording)
'a pet running' is the wordplay.
'running' is an anagram indicator.
'a'+'pet'='apet'
'apet' is an anagram of 'TAPE'.
(Other definitions for tape that I've seen before include "This is often stretched across the finishing line of race" , "Breast this first to win foot-race" , "Race finishing-line" , "Music cassette" , "Record - broken by the winner" .)