Dad worried about second son's speech (7)
I believe the answer is:
address
'speech' is the definition.
(address is a kind of speech)
'dad worried about second son's' is the wordplay.
'worried' is an anagram indicator.
'about' becomes 're' (common abbreviation for 'with reference to').
'second' becomes 's' (common abbreviation).
'dad' with letters rearranged gives 'add'.
'add'+'re'+'s'+'s'='ADDRESS'
(Other definitions for address that I've seen before include "Formal speech" , "Call" , "personal details" , "Give a talk to" , "Begin to deal with" .)