May possibly see a period of renting (8,5)
I believe the answer is:
calendar month
'may possibly' is the definition.
(may is a kind of calendar month)
'see a period of renting' is the wordplay.
I cannot really see how this works, but
'see' could be 'c' (the word for the letter, according to Chambers) and 'c' is found within the answer.
'a' is within the answer.
'period' could be 'month' (month is a kind of period) and 'month' is present in the answer.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for calendar month that I've seen before include "May, for instance" , "all the May days?" , "1 to 31 March, for example" , "May perhaps" , "several weeks" .)