Tenant not so level periodically (6)
I believe the answer is:
lessee
'tenant' is the definition.
(lessee is a kind of tenant)
'not so level periodically' is the wordplay.
'not so' becomes 'less' (I've seen this before).
'periodically' means one should take alternating letters (letters must be selected 'every so often').
The alternate letters of 'level' are 'ee'.
'less'+'ee'='LESSEE'
(Other definitions for lessee that I've seen before include "Tenant with a contract" , "I have to deal with letter" , "One holds a lease" , "Who pays the rent" , "One holding lease on property" .)