Ian McCaskill periodically organised petitions (6)
I believe the answer is:
claims
'petitions' is the definition.
(claim is a kind of petition)
'ian mccaskill periodically organised' is the wordplay.
'periodically' means one should take alternating letters (letters must be selected 'every so often').
'organised' indicates an anagram.
'ian'+'mccaskill'='ianmccaskill'
The alternate letters of 'ianmccaskill' are 'amcsil'.
'amcsil' is an anagram of 'CLAIMS'.
(Other definitions for claims that I've seen before include "States that something is the case" , "Declares that one is the owner of something" , "Asserts as a right" , "States firmly, insisting on truth" , "Assertions of ownership" .)