Senior minister? Blimey, John, shut up! (4,5,4)
I believe the answer is:
lord privy seal
'senior minister?' is the definition.
'Lord Privy Seal' can be an answer for 'minister?' (Lord Privy Seal is an example). I'm not certain of the 'senior' bit.
'blimey john shut up' is the wordplay.
I cannot really see how this works, but
'john' could be 'privy' (synonyms) and 'privy' is located in the answer.
'shut' could be 'seal' (sealing is a kind of shutting) and 'seal' is located in the answer.
The remaining letters 'lord' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for lord privy seal that I've seen before include "UK cabinet minister without specific departmental duties" , "government office" , "Senior cabinet minister" , "Top cabinet minister" , "Cabinet member" .)