For detectives to be after a bit of lunch is very understandable (5)
I believe the answer is:
lucid
'very understandable' is the definition.
'lucid' can be an answer for 'understandable' (synonyms). I'm unsure of the 'very' bit.
'for detectives to be after a bit of lunch' is the wordplay.
'for' becomes 'u' (I can't explain this - if you can you should believe this answer much more).
'detectives' becomes 'CID' (abbreviation for Criminal Investigation Department).
'to be after' is a charade indicator (letters next to each other).
'a bit of' suggests taking the first letters.
The first letter of 'lunch' is 'l'.
'u'+'cid'='ucid'
'ucid' after 'l' is 'LUCID'.
'is' is the link.
Can you help me to learn more?
(Other definitions for lucid that I've seen before include "Limpid" , "completely clear" , "Clear and comprehensible" , "Rational, clear" , "Readily understood" .)