Crossword Genius

Place once for storage in Bath with term almost up (5,4)

Ross

I believe the answer is:

tithe barn

I'm a little stuck... Click here to teach me more about this clue!

'place once for storage' is the definition.
Although both the answer and definition are singular nouns, I cannot understand how they can define each other.

'in bath with term almost up' is the wordplay.
'with' means one lot of letters go next to another.
'almost' means to remove the last letter (most of the word but not all of it).
'up' indicates anagramming the letters (letters get chucked up).
'term' with its last letter taken off is 'ter'.
'in'+'bath'='inbath'
'inbath' put after 'ter' is 'terinbath'.
'terinbath' is an anagram of 'TITHE-BARN'.

Can you help me to learn more?

(Other definitions for tithe barn that I've seen before include "somewhere in farm" , "Church tax store" , "Store for dues to church" , "historic building?" , "Store for produce given to the church" .)

I've seen this clue in The Times.
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