Recording a pet playing (4)
I believe the answer is:
tape
'recording' is the definition.
(tape is a kind of recording)
'a pet playing' is the wordplay.
'playing' is an anagram indicator.
'a'+'pet'='apet'
'apet' anagrammed gives 'TAPE'.
(Other definitions for tape that I've seen before include "Breast this first to win a race" , "Ribbon" , "Race finishing-line" , "The winning runner breasts the ...." , "Race finishing line strip" .)