Periodically verge on conceit (3)
I believe the answer is:
ego
'conceit' is the definition.
(I've seen this in another clue)
'periodically verge on' is the wordplay.
'periodically' means one should take alternating letters (letters must be selected 'every so often').
'verge'+'on'='vergeon'
The alternating letters of 'vergeon' are 'EGO'.
(Other definitions for ego that I've seen before include "Inflated pride" , "Sense of identity" , "Inner self" , "One's sense of self-importance" , "Conscious mind" .)