She plays a major part in a Shaw play (7)
I believe the answer is:
barbara
'a shaw play' is the definition.
The definition suggests a singular noun which matches the answer.
'she plays a major part' is the wordplay.
'she' becomes 'Barb'.
'plays a major part' becomes 'ara' (I am not sure about this - if you are sure you should believe this answer much more).
'barb'+'ara'='BARBARA'
'in' acts as a link.
Can you help me to learn more?
(Other definitions for barbara that I've seen before include "Girl's name" , "Major -, (G.B. Shaw)" , "Dame - Cartland, English author" , "Major -, (G. B. Shaw)" , "Major --, play by Shaw" .)