Town lady, short of oxygen, getting agitated in Parliament (7)
I believe the answer is:
tynwald
'parliament' is the definition.
(I've seen this before)
'town lady short of oxygen getting agitated' is the wordplay.
'short of' indicates named letters should be taken away.
'oxygen' becomes 'O' (atomic symbol for oxygen).
'getting agitated' indicates anagramming the letters.
'town'+'lady'='townlady'
'townlady' with 'o' removed is 'twnlady'.
'twnlady' anagrammed gives 'TYNWALD'.
'in' acts as a link.
(Other definitions for tynwald that I've seen before include "Manx parliament" , "Parliament of Isle of Man" , "IoM parliament" , "Governing assembly of the Isle of Man" , "Man is governed by this" .)