A fraction enter the inn drunk, then run away (10)

I believe the answer is:

nineteenth

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'away' is the definition.
Both the answer and definition are adjectives. Perhaps there's a link between them I don't understand?

'a fraction enter the inn drunk then run' is the wordplay.
'a fraction' becomes 'ete' (I can't justify this - if you can you should give a lot more credence to this answer).
'enter' is an insertion indicator.
'drunk' indicates an anagram.
'run' indicates anagramming the letters.
'inn' is an anagram of 'nin'.
'then' with letters rearranged gives 'enth'.
'nin'+'enth'='ninenth'
'ete' going inside 'ninenth' is 'NINETEENTH'.

Can you help me to learn more?

(Other definitions for nineteenth that I've seen before include "Golf club's bar" , "irrepressibly talking?" .)

I've seen this clue in The Guardian.

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