Have tenant periodically (3)
I believe the answer is:
eat
'have' is the definition.
(have can mean to eat or consume)
'tenant periodically' is the wordplay.
'periodically' indicates alternate letters (letters must be selected 'every so often').
The alternating letters of 'tenant' are 'EAT'.
(Other definitions for eat that I've seen before include "tolerate in diet" , "Ingest" , "Use a knife and fork" , "Consume for tea" , "Do cats - bats? Do bats - cats? (Alice in Wonderland)" .)