Pets regularly bite? Avoid! (6)
I believe the answer is:
eschew
'avoid' is the definition.
(eschewing is a kind of avoiding)
'pets regularly bite?' is the wordplay.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'bite?' becomes 'chew' (chew is a kind of bite).
The alternating letters of 'pets' are 'es'.
'es'+'chew'='ESCHEW'
(Other definitions for eschew that I've seen before include "'Stay clear of, shun (6)'" , "Shun, spurn" , "Avoid or abstain from, food or people" , "'Avoid, stay away from (6)'" , "Ignore" .)