Spot where time’s up? (5,5)

I believe the answer is:
clock tower
'spot' is the definition.
I know nothing about this answer so I cannot judge whether this works.
'time's up?' is the wordplay.
I cannot quite see how this works, but
'time' could be 'clock' (synonyms) and 'clock' is found within the answer.
The remaining letters 'tower' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
'where' acts as a link.
Can you help me to learn more?
(Other definitions for clock tower that I've seen before include "Big Ben, for example" , "will it hold up the enemy's progress?" , "one looked up to for a time?" .)
