Letter or article by the one-time Ms Lynch (4)
I believe the answer is:
'letter' is the definition.
(beta is a kind of letter)
'article by the one-time ms lynch' is the wordplay.
I cannot quite understand how this works, but
'article' could be 'a' (the indefinite article in English) and 'a' is found within the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is present in the answer.
The remaining letters 'be' is a valid word which might be clued in a way I don't see.
This may be the basis of clue (or it may be nonsense).
'or' acts as a link.
Can you help me to learn more?
(Other definitions for beta that I've seen before include "Old character", "Character between alpha and gamma", "Letter before gamma", "software under test", "second class grade?".)