Restricted time, perhaps, in cover (7)
I believe the answer is:
limited
'restricted' is the definition.
('limit' can be a synonym of 'restrict')
'time perhaps in cover' is the wordplay.
'perhaps' indicates anagramming the letters.
'in' means one lot of letters goes inside another.
'cover' becomes 'lid' (lid is a kind of cover**).
'time' is an anagram of 'mite'.
'mite' put inside 'lid' is 'LIMITED'.
(Other definitions for limited that I've seen before include "Sort of company" , "Checked" , "Confined within bounds" , "Constrained" , "Narrow" .)