Emotional rent boy's base (5)

I believe the answer is:

teary

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'emotional' is the definition.
(likely to burst into tears)

'rent boy's base' is the wordplay.
'rent' becomes 'tear' (synonyms).
'boy's base' becomes 'y' (I can't justify this - if you can you should give a lot more credence to this answer).
'tear'+'y'='TEARY'

Can you help me to learn more?

(Other definitions for teary that I've seen before include "Crying" , "Weeping" , "Upset" , "Watery" , "Emotional" .)

I've seen this clue in The Times.

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