Small nurses seek at first to care for boxers? (3-3)

'care for boxers?' is the definition.
(pet-sitting could mean looking after boxer dogs)

'small nurses seek at first' is the wordplay.
'small' becomes 'petit' (I've seen this before).
'nurses' indicates putting letters inside (nurse can mean to hold onto or harbour).
'at first' suggests taking the first letters.
The initial letter of 'seek' is 's'.
'petit' placed around 's' is 'PET-SIT'.

'to' acts as a link.