Worries about small pet (6)
I believe the answer is:
caress
'pet' is the definition.
(thesaurus)
'worries about small' is the wordplay.
'worries' becomes 'cares' (I've seen this before).
'about' indicates putting letters inside.
'small' becomes 's' (abbreviation - e.g. clothes size).
'cares' going around 's' is 'CARESS'.
(Other definitions for caress that I've seen before include "Gentle loving touch" , "Stroke fondly" , "show of affection" , "Pat" , "Stroke lovingly" .)