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' says to put 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" .)