Regularly applies to be seen with a petition (4)
I believe the answer is:
plea
'petition' is the definition.
(I've seen this before)
'regularly applies to be seen with a' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'to be seen with' means one lot of letters go next to another.
The alternating letters of 'applies' are 'ple'.
'ple'+'a'='PLEA'
(Other definitions for plea that I've seen before include "Urgent entreaty" , "Excuse, entreaty" , "Heartfelt request" , "Dispute" , "Petition or supplication" .)