In reality, this is unwelcome to hear (4,5)

I believe the answer is:

home truth

'this is unwelcome to hear' is the definition.

'in reality' is the wordplay.
'in' becomes 'home' ('he's in' can mean 'he's home').
'reality' becomes 'truth'.
'home'+'truth'='HOME TRUTH'

(Other definitions for home truth that I've seen before include "Blunt statement" , "Unpleasant fact person is made to realise about himself" , "unwelcome fact - with 24a" , "Unpleasant fact told to someone about themselves" , "Pointed statement" .)

I've seen this clue in The Times.

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