Of high rank in the CID - immortal, in fact (5)
I believe the answer is:
cupid
'immortal in fact' is the definition.
'Cupid' can be an answer for 'immortal' (Cupid is an example). I am not sure about the 'in fact' bit.
'of high rank in the cid' is the wordplay.
I cannot quite see how this works, but
'high' could be 'up' (associated in meaning) and 'up' is found in the answer.
'the cid' could be 'cid' and 'cid' is located in the leftover letters.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for cupid that I've seen before include "a help to Santa" , "boy with little bow" , "Armed boy" , "Blind god" , "heathen god" .)