Crossword Genius

Led astray on fringes, portion of cathedral ran out (7)

Ross

I believe the answer is:

elapsed

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'ran out' is the definition.
(I've seen this in another clue)

'led astray on fringes portion' is the wordplay.
'astray' indicates anagramming the letters.
'on' indicates putting letters inside (as in clothing 'on' a person).
'fringes portion' becomes 'apse' (I can't justify this - if you can you should believe this answer much more).
'led' is an anagram of 'eld'.
'eld' going around 'apse' is 'ELAPSED'.

'of cathedral' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for elapsed that I've seen before include "Passed, of time" , "Went by" , "slipped away" , "Pleased (anag.)" , "Pleased to have passed" .)

I've seen this clue in The Independent.
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