Much-loved dad, initially up late and reading (7)
I believe the answer is:
popular
'much-loved' is the definition.
'dad initially up late and reading' is the wordplay.
'dad' becomes 'pop' ('pop' can be a synonym of 'dad'**).
'initially' says to take the initial letters.
The initial letters of 'up late and reading' is 'ular'.
'pop'+'ular'='POPULAR'
(Other definitions for popular that I've seen before include "appealing to the public" , "Fashionable" , "having many fans" , "In demand" , "The people's" .)