Provide pet with hesitation (5)
I believe the answer is:
cater
'provide' is the definition.
(I know that provide can be written as cater)
'pet with hesitation' is the wordplay.
'pet' becomes 'cat' (cats are often kept as pets).
'with' means one lot of letters go next to another.
'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" .)