Clue is tenuous, time to finish! (4)
I believe the answer is:
hint
'clue' is the definition.
('hint' can be a synonym of 'clue')
'tenuous time to finish' is the wordplay.
'tenuous' becomes 'thin' ('thin' can be similar in meaning to 'tenuous').
'time' becomes 't'.
'to finish' means to remove the first letter.
'thin'+'t'='thint'
'thint' with its initial letter removed is 'HINT'.
'is' is the link.
(Other definitions for hint that I've seen before include "CRT screen coating" , "signal" , "Indirect clue" , "Thin sort of slight indication" , "Intimate" .)