Extend the period of time (7)
I believe the answer is:
stretch
This clue is a triple definition!
'extend' is the first definition.
(I know that extend can be written as stretch)
'the period' is the second definition.
(stretch is a kind of period)
'of' is a link.
'time' is the third definition.
(I've seen this before)
(Other definitions for stretch that I've seen before include "Period of time in prison" , "sort of limousine" , "Increase" , "Elasticity, prison term" , "Make longer/wider" .)