Green light from department principal for one of those in Trinity
I believe the answer is:
godhead
'trinity' is the definition.
(I've seen this before)
'green light from department principal for one of' is the wordplay.
'green light' becomes 'go' (I've seen this in other clues).
'from' means one lot of letters go next to another.
'principal' suggests taking the first letters.
'for' says to put letters next to each other.
'one of' becomes 'head' (I can't explain this - if you can you should believe this answer much more).
The first letter of 'department' is 'd'.
'go'+'d'+'head'='GODHEAD'
'those in' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for godhead that I've seen before include "deity" , "Had doge partaken or divine nature?" , "Trinity" , "Creator" .)