Provide pet with hesitation (5)
I believe the answer is:
cater
'provide' is the definition.
(I know that cater is a more specific form of provide)
'pet with hesitation' is the wordplay.
'pet' becomes 'cat' (cats are often kept as pets).
'with' is a charade indicator (letters next to each other).
'hesitation' becomes 'er' (sound made while hesitating - um, er).
'cat'+'er'='CATER'
(Other definitions for cater that I've seen before include "Provide service for like grocer" , "Provide what is needed or wanted" , "Supply food for parties" , "so put out food?" , "Supply food and drink" .)