Pets' tension nearly overwhelms vet (7)

'pets'' is the definition.
(I've seen this in another clue)

'tension nearly overwhelms vet' is the wordplay.
'tension' becomes 'stress' (synonyms).
'nearly' means to remove the last letter.
'overwhelms' means one lot of letters goes inside another.
'vet' becomes 'OK' (OK can mean to approve or vet).
'stress' with its last letter taken off is 'stres'.
'stres' enclosing 'ok' is 'STROKES'.