The old man’s at half pace again (4)
I believe the answer is:
papa
'the old man's' is the definition.
('papa' can be a synonym of 'old man')
'at half pace again' is the wordplay.
'at' is a charade indicator (letters next to each other).
'half' indicates taking half.
'again' becomes 'pa' (I can't justify this - if you can you should give a lot more credence to this answer).
'pace' cut in half is 'pa'.
'pa' put next to 'pa' is 'PAPA'.
Can you help me to learn more?
(Other definitions for papa that I've seen before include "Mama's other half?" , "Comms code for 'P'" , "Pop" , "The old man" , "Father; P (radio comms.)" .)