Periodically verge on conceit (3)
I believe the answer is:
ego
'conceit' is the definition.
(I've seen this before)
'periodically verge on' is the wordplay.
'periodically' indicates alternate 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" .)