... diplomat not wanted as Republican in Pentagon, NASA or otherwise (7,3,5)
I believe the answer is:
persona non grata
'diplomat' is the definition.
(persona non grata is a kind of diplomat)
'republican in pentagon nasa or otherwise' is the wordplay.
'republican' becomes 'r' (abbreviation).
'in' means one lot of letters goes inside another.
'otherwise' is an anagram indicator.
'pentagon'+'nasa'+'or'='pentagonnasaor'
'pentagonnasaor' with letters rearranged gives 'personanongata'.
'r' placed into 'personanongata' is 'PERSONA NON GRATA'.
'not wanted as' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for persona non grata that I've seen before include "Undesirable" , "One banned" .)