When sick, try and eat - with a day off though, whatever may happen (2,3,4)
I believe the answer is:
at any rate
'whatever may happen' is the definition.
(I've seen this before)
'when sick try and eat with a' is the wordplay.
'when' becomes 'a' (I can't justify this - if you can you should give a lot more credence to this answer).
'sick' is an anagram indicator.
'and' means one lot of letters go next to another.
'with' indicates putting letters inside.
'a' becomes 'an'.
'try'+'eat'='tryeat'
'tryeat' anagrammed gives 'tyrate'.
'tyrate' enclosing 'an' is 'tanyrate'.
'a'+'tanyrate'='AT ANY RATE'
'day off though' 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.
(Other definitions for at any rate that I've seen before include "regardless of the speed" , "Whatever may happen" , "Whatever happens" , "regardless of the cost?" , "In whatever case" .)